Discrete memristive neuron systems have attracted considerable attention due to their nonlinear dynamical properties,low computational overhead,and ease of hardware implementation.For the practical engineering applica...Discrete memristive neuron systems have attracted considerable attention due to their nonlinear dynamical properties,low computational overhead,and ease of hardware implementation.For the practical engineering applications of discrete memristive neuron systems,effective control remains a key issue.Parameter identification using intelligent optimization algorithms is an important approach for controlling complex nonlinear systems.However,classical algorithms are prone to falling into local optima and often exhibit high computational complexity,resulting in slow convergence.Therefore,a new algorithm named adaptive chaos game optimization(ACGO)is proposed to address these issues.By introducing a differential evolution mutation strategy and a Cauchy adaptive parameter mechanism,the ACGO algorithm can effectively balance global exploration and local exploitation capabilities.To verify the effectiveness of the proposed algorithm,it is applied to parameter identification in five discrete memristive neuron maps(DMNMs)and compared with seven intelligent optimization algorithms.Simulation results demonstrate that the ACGO algorithm achieves higher accuracy and faster convergence.In addition,an in-depth investigation is conducted into the effects of sample size and objective function on identification performance.The results indicate that setting the sample size to 4 and selecting the mean squared error(MSE)as the objective function can achieve better identification performance and a high level of robustness.展开更多
In this paper,we obtain the dichotomy between mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space.The mean Li-Yorke chaos for sequences and ...In this paper,we obtain the dichotomy between mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space.The mean Li-Yorke chaos for sequences and submultiplicative sequences of bounded linear operators are also studied.Furthermore,several criteria for mean Li-Yorke chaos are established.展开更多
The study of relationship emotions,a set of emotional and psychological responses that arise in a relationship,can help develop more humanized artificial intelligence,improve human–computer interaction,and even creat...The study of relationship emotions,a set of emotional and psychological responses that arise in a relationship,can help develop more humanized artificial intelligence,improve human–computer interaction,and even create more immersive experiences in virtual and augmented reality.Due to the nonlinear and feedback-driven nature of relational affect,which aligns closely with chaos theory,and the ability of leaky integrate-and-fire(LIF)neuron models to simulate dopaminerelated electrical activity in brain nuclei,this study innovatively integrates both approaches.By linking the membrane potential signals of LIF neurons to relational affect equations,it achieves a refined modeling of the mechanisms underlying relational affect generation.This paper adds the LIF neuron model to the relationship emotion model to construct a new LIF relationship emotion model(LRM).The effect of the parameters in the LRM on the relationship emotions generated by the model is investigated using numerical analysis.This includes the firing behavior produced by LIF neurons and a study of relationship emotions produced by different initial relationship emotion states under the same conditions.Finally,the feasibility of LRM is verified using a digital signal processing(DSP)platform.This process not only verifies the feasibility of LRM but also provides new ideas and methods for future research in affective computing and human–computer interaction.展开更多
Omnivory,where species feed across multiple trophic levels,is a widespread feature of ecological networks.A key mechanism underlying such complexity is intraguild predation(IGP),in which a top predator consumes both a...Omnivory,where species feed across multiple trophic levels,is a widespread feature of ecological networks.A key mechanism underlying such complexity is intraguild predation(IGP),in which a top predator consumes both an intermediate predator and a shared resource.Here,we show that Shilnikov homoclinic orbits emerge in a minimal intraguild predation model,triggering a cascade of homoclinic bifurcations near a saddle-focus equilibrium that culminates in chaos.Numerical simulations and Lyapunov spectrum analysis reveal multiple coexistence modes,ranging from regular oscillations to Shilnikov homoclinic orbits and chaos.Our model quantitatively reproduces patterns observed in natural omnivore networks,providing mechanistic insights into complex population fluctuations in ecological systems.展开更多
The dynamics of heart rhythms plays a pivotal role in physiological health,where chaotic behavior is often associated with pathological cardiac states.In this work,we investigate a fractional-order model of cardiac pa...The dynamics of heart rhythms plays a pivotal role in physiological health,where chaotic behavior is often associated with pathological cardiac states.In this work,we investigate a fractional-order model of cardiac pacemaker dynamics using incommensurate derivatives to capture the complex memory effects and non-local interactions inherent in biological systems.We demonstrate that slight variations in the fractional orders induce rich dynamics,including chaos and coexisting attractors,signifying transitions between normal and dysfunctional rhythms.Crucially,our model exhibits wider chaotic regions than classical integer-order counterparts when the incommensurate derivatives are perturbed.Furthermore,we reveal pronounced multistability,where distinct chaotic attractors coexist under identical parameters,reflecting the system's capacity for abrupt transitions between physiological and pathological states.These findings advance the mechanistic understanding of rhythm disorders and highlight the critical role of fractional calculus in modeling cardiac dynamics.展开更多
We numerically study three-dimensional acoustic cavities with progressively increasing geometric complexity and analyze their spectral and spatial statistics.The eigenfrequency spectra and adjacent level-spacing ratio...We numerically study three-dimensional acoustic cavities with progressively increasing geometric complexity and analyze their spectral and spatial statistics.The eigenfrequency spectra and adjacent level-spacing ratios reveal a clear transition from Poisson to Gaussian orthogonal ensemble(GOE)statistics as the cavity structure becomes more irregular.The intermediate regimes are quantitatively characterized using the Berry–Robnik(BR)and Brody distributions,which yield consistent estimates of the chaotic fraction.Furthermore,both the participation ratio and long-range spectral correlations confirm the continuous evolution from integrable to chaotic dynamics.The distributions of normalized wavefunction amplitudes gradually approach the Gaussian prediction,indicating the onset of wave chaos.These results demonstrate that three-dimensional acoustic resonators provide a numerically controllable and experimentally accessible platform for studying the universal transition from Poisson to GOE statistics and for exploring the interplay between geometry and wave chaos.展开更多
This paper employs the Lattice Boltzmann Method(LBM)to investigate the nonlinear characteristics of natural convection in toroidal spaces with radius ratios of 2.6,1.6,1.4,and 1.2.Based on the maximum Lyapunov exponen...This paper employs the Lattice Boltzmann Method(LBM)to investigate the nonlinear characteristics of natural convection in toroidal spaces with radius ratios of 2.6,1.6,1.4,and 1.2.Based on the maximum Lyapunov exponent,runs test,and phase space trajectory,the transition from steady-state to chaotic state is analyzed.The results show that with increasing Rayleigh number(Ra),the toroidal system successively experiences a steady state,a periodic oscillation state,a quasi-periodic oscillation state,and finally enters a chaotic state.For example,when the radius ratio is 2.6,these transitions occur at Ra values of 5×105,1.5×106,2.1×106,and 2.5×106,respectively.Furthermore,the study finds that decreasing the radius ratio significantly lowers the critical Rayleigh number,indicating an increased sensitivity of the system to geometry.Moreover,under the same radius ratio and system state,the critical Rayleigh number for a concentric toroidal cavity is consistently higher than that for an eccentric toroidal cavity.These results quantitatively reveal the role of geometric parameters in controlling flow instability and the occurrence of chaos in toroidal convection systems.展开更多
The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this...The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this study proposes an innovative hybrid approach that integrates wavelet neural network(WNN)with chaos analysis.By leveraging the Cross-Correlation(C−C)method,the minimum embedding dimension for phase space reconstruction is systematically calculated and then adopted as the input node configuration for the WNN.Simulation results demonstrate the remarkable effectiveness of this integrated method in predicting pressure drop signals,advancing our understanding of the intricate dynamic phenomena occurring with V−L−S fluidized bed evaporators.Moreover,this study offers a novel perspective on applying advanced data-driven techniques to handle the complexities of multi-phase flow systems and highlights the potential for improved operational prediction and control in industrial settings.展开更多
In response to the accelerating demands of industrial development,the scale-up of stirred reactors has become increasingly prevalent.Multi-shaft stirred reactors have emerged as a promising solution;however,a critical...In response to the accelerating demands of industrial development,the scale-up of stirred reactors has become increasingly prevalent.Multi-shaft stirred reactors have emerged as a promising solution;however,a critical challenge remains in achieving efficient mixing while simultaneously minimizing energy consumption.Here,a novel approach based on differential rotation speeds to optimize mixing performance was proposed.Results demonstrate that a carefully configured rotation speed difference significantly enhances mixing efficiency,reducing mixing time by 17.89% and power consumption by 12.07%.This strategy not only amplifies flow field instability but also minimizes instability discrepancies,promoting a more uniform distribution of vortices across various scales.Furthermore,under this approach,the bottom impeller has the strongest impact on mixing,while the middle and lower impellers synergistically strengthen the weaker mixing regions and facilitate the redistribution of energy in the flow field.This method promotes efficient energy transfer from large-scale to small-scale vortices,ultimately improving overall mixing performance.This work offers a promising avenue for the optimal design and operation of multi-shaft stirred reactors,advancing both efficiency and energy sustainability.展开更多
Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the l...Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.展开更多
This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-...This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.展开更多
Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be wr...Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.展开更多
This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investi...This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.展开更多
This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging...This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.展开更多
We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise durin...We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise during the photoelectric detection and analog-digital conversion,the varying of output optical power would change the signal to noise ratio,then impact time delay signature identification and the random bit generation.Our results show that,when the optical power is less than-14 dBm,with the decreasing of the optical power,the actual identified time delay signature degrades and the entropy of the chaotic signal increases.Moreover,the extracted random bit sequence with lower optical power is more easily pass through the randomness testing.展开更多
The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break...The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.展开更多
As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road ...As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H2 robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H2 robust controller not only provides better performance in terms of vehicle ride comfort compared to general H2 robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.展开更多
Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonanc...Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.展开更多
Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting ...Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, km;shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, km, ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.展开更多
In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between t...In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between the k-tensor product ft■kof the solution to be Linear-Formation kinetic equation and the k-marginal fN,ktof the solution to the Liouville equation corresponding to the Linear-Formation particle model.Specifically,the following estimate holds in terms of p-Wasserstein(1≤p<∞)distance Wpp(ft■k,fN,kt)≤C1k/Nmin(p/2,1)(1+tp)e^(C2t),1≤k≤N.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.62501516 and 62572419)the Natural Science Foundation of Hunan Province(Grant Nos.2025JJ50391 and 2025JJ50392)the Research Foundation of the Education Department of Hunan Province(Grant Nos.23B0131 and 24A0124)。
摘要Discrete memristive neuron systems have attracted considerable attention due to their nonlinear dynamical properties,low computational overhead,and ease of hardware implementation.For the practical engineering applications of discrete memristive neuron systems,effective control remains a key issue.Parameter identification using intelligent optimization algorithms is an important approach for controlling complex nonlinear systems.However,classical algorithms are prone to falling into local optima and often exhibit high computational complexity,resulting in slow convergence.Therefore,a new algorithm named adaptive chaos game optimization(ACGO)is proposed to address these issues.By introducing a differential evolution mutation strategy and a Cauchy adaptive parameter mechanism,the ACGO algorithm can effectively balance global exploration and local exploitation capabilities.To verify the effectiveness of the proposed algorithm,it is applied to parameter identification in five discrete memristive neuron maps(DMNMs)and compared with seven intelligent optimization algorithms.Simulation results demonstrate that the ACGO algorithm achieves higher accuracy and faster convergence.In addition,an in-depth investigation is conducted into the effects of sample size and objective function on identification performance.The results indicate that setting the sample size to 4 and selecting the mean squared error(MSE)as the objective function can achieve better identification performance and a high level of robustness.
基金suported in part by the NSF of China(12222110)supported in part by the NSF of China(12301230)+1 种基金the STU Scientific Research Initiation Grant(SRIG,NTF22020)supported by the NSF of China(12301226).
摘要In this paper,we obtain the dichotomy between mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space.The mean Li-Yorke chaos for sequences and submultiplicative sequences of bounded linear operators are also studied.Furthermore,several criteria for mean Li-Yorke chaos are established.
基金supported by the National Natural Science Foundation of China(Grant No.62571079)the Doctoral Research Startup Fund Program Project of Liaoning Province(Grant No.2025-BS-0471)+1 种基金the Basic scientific research projects in department of education of Liaoning Province(Grant No.LJ212410152011)the Research startup fund project for introducing talents of Dalian Polytechnic University(Grant No.LJBKY2025070)。
摘要The study of relationship emotions,a set of emotional and psychological responses that arise in a relationship,can help develop more humanized artificial intelligence,improve human–computer interaction,and even create more immersive experiences in virtual and augmented reality.Due to the nonlinear and feedback-driven nature of relational affect,which aligns closely with chaos theory,and the ability of leaky integrate-and-fire(LIF)neuron models to simulate dopaminerelated electrical activity in brain nuclei,this study innovatively integrates both approaches.By linking the membrane potential signals of LIF neurons to relational affect equations,it achieves a refined modeling of the mechanisms underlying relational affect generation.This paper adds the LIF neuron model to the relationship emotion model to construct a new LIF relationship emotion model(LRM).The effect of the parameters in the LRM on the relationship emotions generated by the model is investigated using numerical analysis.This includes the firing behavior produced by LIF neurons and a study of relationship emotions produced by different initial relationship emotion states under the same conditions.Finally,the feasibility of LRM is verified using a digital signal processing(DSP)platform.This process not only verifies the feasibility of LRM but also provides new ideas and methods for future research in affective computing and human–computer interaction.
基金supported by National Natural Science Foundation of China(Grant Nos.12474207,T2522042)。
摘要Omnivory,where species feed across multiple trophic levels,is a widespread feature of ecological networks.A key mechanism underlying such complexity is intraguild predation(IGP),in which a top predator consumes both an intermediate predator and a shared resource.Here,we show that Shilnikov homoclinic orbits emerge in a minimal intraguild predation model,triggering a cascade of homoclinic bifurcations near a saddle-focus equilibrium that culminates in chaos.Numerical simulations and Lyapunov spectrum analysis reveal multiple coexistence modes,ranging from regular oscillations to Shilnikov homoclinic orbits and chaos.Our model quantitatively reproduces patterns observed in natural omnivore networks,providing mechanistic insights into complex population fluctuations in ecological systems.
摘要The dynamics of heart rhythms plays a pivotal role in physiological health,where chaotic behavior is often associated with pathological cardiac states.In this work,we investigate a fractional-order model of cardiac pacemaker dynamics using incommensurate derivatives to capture the complex memory effects and non-local interactions inherent in biological systems.We demonstrate that slight variations in the fractional orders induce rich dynamics,including chaos and coexisting attractors,signifying transitions between normal and dysfunctional rhythms.Crucially,our model exhibits wider chaotic regions than classical integer-order counterparts when the incommensurate derivatives are perturbed.Furthermore,we reveal pronounced multistability,where distinct chaotic attractors coexist under identical parameters,reflecting the system's capacity for abrupt transitions between physiological and pathological states.These findings advance the mechanistic understanding of rhythm disorders and highlight the critical role of fractional calculus in modeling cardiac dynamics.
基金supported by the National Natural Science Foundation of China(Grant Nos.11775100,12247101,11961131009)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2025-jdzx07)+2 种基金the Natural Science Foundation of Gansu Province(Grant Nos.22JR5RA389 and 25JRRA799)the‘111 Center’under Grant No.B20063financial support from the China Scholarship Council(Grant No.CSC-202306180087)。
摘要We numerically study three-dimensional acoustic cavities with progressively increasing geometric complexity and analyze their spectral and spatial statistics.The eigenfrequency spectra and adjacent level-spacing ratios reveal a clear transition from Poisson to Gaussian orthogonal ensemble(GOE)statistics as the cavity structure becomes more irregular.The intermediate regimes are quantitatively characterized using the Berry–Robnik(BR)and Brody distributions,which yield consistent estimates of the chaotic fraction.Furthermore,both the participation ratio and long-range spectral correlations confirm the continuous evolution from integrable to chaotic dynamics.The distributions of normalized wavefunction amplitudes gradually approach the Gaussian prediction,indicating the onset of wave chaos.These results demonstrate that three-dimensional acoustic resonators provide a numerically controllable and experimentally accessible platform for studying the universal transition from Poisson to GOE statistics and for exploring the interplay between geometry and wave chaos.
摘要This paper employs the Lattice Boltzmann Method(LBM)to investigate the nonlinear characteristics of natural convection in toroidal spaces with radius ratios of 2.6,1.6,1.4,and 1.2.Based on the maximum Lyapunov exponent,runs test,and phase space trajectory,the transition from steady-state to chaotic state is analyzed.The results show that with increasing Rayleigh number(Ra),the toroidal system successively experiences a steady state,a periodic oscillation state,a quasi-periodic oscillation state,and finally enters a chaotic state.For example,when the radius ratio is 2.6,these transitions occur at Ra values of 5×105,1.5×106,2.1×106,and 2.5×106,respectively.Furthermore,the study finds that decreasing the radius ratio significantly lowers the critical Rayleigh number,indicating an increased sensitivity of the system to geometry.Moreover,under the same radius ratio and system state,the critical Rayleigh number for a concentric toroidal cavity is consistently higher than that for an eccentric toroidal cavity.These results quantitatively reveal the role of geometric parameters in controlling flow instability and the occurrence of chaos in toroidal convection systems.
基金supported by the open foundation of State Key Laboratory of Chemical Engineering(SKL-ChE-22B01)the Natural Science Foundation of China(22008169).
摘要The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this study proposes an innovative hybrid approach that integrates wavelet neural network(WNN)with chaos analysis.By leveraging the Cross-Correlation(C−C)method,the minimum embedding dimension for phase space reconstruction is systematically calculated and then adopted as the input node configuration for the WNN.Simulation results demonstrate the remarkable effectiveness of this integrated method in predicting pressure drop signals,advancing our understanding of the intricate dynamic phenomena occurring with V−L−S fluidized bed evaporators.Moreover,this study offers a novel perspective on applying advanced data-driven techniques to handle the complexities of multi-phase flow systems and highlights the potential for improved operational prediction and control in industrial settings.
基金supported by the National Natural Science Foundation of China (22078030,52021004)National Key Research and Development Project (2019YFC1905802)+4 种基金Key Project of Independent Research Project of State Key Laboratory of Coal Mine Disaster Dynamics and Control (2011DA105287-zd201902)Chongqing Natural Science Foundation Innovation and Development Joint Fund Project (CSTB2022NSCQ-LZX0014)Hubei Three Gorges Laboratory Open/Innovation Fund (SK211009,SK215001)Fundamental Research Funds for Central Universities(2022CDJQY-005)this work also received funding from the China Scholarship Council。
摘要In response to the accelerating demands of industrial development,the scale-up of stirred reactors has become increasingly prevalent.Multi-shaft stirred reactors have emerged as a promising solution;however,a critical challenge remains in achieving efficient mixing while simultaneously minimizing energy consumption.Here,a novel approach based on differential rotation speeds to optimize mixing performance was proposed.Results demonstrate that a carefully configured rotation speed difference significantly enhances mixing efficiency,reducing mixing time by 17.89% and power consumption by 12.07%.This strategy not only amplifies flow field instability but also minimizes instability discrepancies,promoting a more uniform distribution of vortices across various scales.Furthermore,under this approach,the bottom impeller has the strongest impact on mixing,while the middle and lower impellers synergistically strengthen the weaker mixing regions and facilitate the redistribution of energy in the flow field.This method promotes efficient energy transfer from large-scale to small-scale vortices,ultimately improving overall mixing performance.This work offers a promising avenue for the optimal design and operation of multi-shaft stirred reactors,advancing both efficiency and energy sustainability.
基金funded by Taif University,Saudi Arabia,Project No.(TU-DSPP-2024-52).
摘要Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.
基金support from the National Natural Science Foundation of China(Grant Nos.52174123&52274222).
摘要This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.
基金supported by the National Natural Science Foundation of China under Grant No.12122515(HH)Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(Grant No.2022B1212010008)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023B1515040023)。
摘要Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.
基金Project supported by the National Nature Science Foundation of China (Grant No 60574036), the Specialized Research Fund for the Doctoral Program of China (Grant No 20050055013) and the Program for New Excellent Talents in University of China (NCET).
摘要This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.
基金supported by Young Talents from Longyuan,Gansu Province(Liwei Liu),the Fundamental Research Funds for the Central Universities,Northwest Minzu University(Grant No.31920230134)Teaching Achievement Cultivation Project of Gansu Province Department of Education(Grant No.2022GSJXCGPY-46)+1 种基金Special research topic on curriculum and teaching materials for primary,secondary and higher schools,Gansu Province Department of Education(Grant No.GSJC-Y2024204)Quality improvement project for undergraduate talent training,Northwest Minzu University(Grant Nos.2024YBJG-04 and 2024FCTD-03).
摘要This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.
基金Project supported in part by the National Natural Science Foundation of China(Grant Nos.62005129 and 62175116)。
摘要We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise during the photoelectric detection and analog-digital conversion,the varying of output optical power would change the signal to noise ratio,then impact time delay signature identification and the random bit generation.Our results show that,when the optical power is less than-14 dBm,with the decreasing of the optical power,the actual identified time delay signature degrades and the entropy of the chaotic signal increases.Moreover,the extracted random bit sequence with lower optical power is more easily pass through the randomness testing.
基金support from the National Natural Science Foundation of China(Nos.12102242 and 12172086)the Educational Foundation of Liaoning Province(No.JYTQN2023261)the Key R&D Program of Shandong Province of China(No.2022SFGC0801).
摘要The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.
基金Supported by National Natural Science Foundation of China(Grant No.51875256)Open Platform Fund of Human Institute of Technology(Grant No.KFA22009).
摘要As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H2 robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H2 robust controller not only provides better performance in terms of vehicle ride comfort compared to general H2 robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.
摘要Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.
基金Dalian Municipal Natural Science Foundation under Grant No.2019RD01。
摘要Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, km;shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, km, ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.
基金supported by the Natural Science Foundation of Hunan Province(2022JJ30655)the National Natural Science Foundation of China(12371180)the Training Program for Excellent Young Innovators of Changsha(kq2305046)。
摘要In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between the k-tensor product ft■kof the solution to be Linear-Formation kinetic equation and the k-marginal fN,ktof the solution to the Liouville equation corresponding to the Linear-Formation particle model.Specifically,the following estimate holds in terms of p-Wasserstein(1≤p<∞)distance Wpp(ft■k,fN,kt)≤C1k/Nmin(p/2,1)(1+tp)e^(C2t),1≤k≤N.