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Turing Patterns in a Reaction-Diffusion System 认领 引用
1
作者 WU Yan-Ning WANG Ping-Jian HOU Chun-Ju LIU Chang-Song ZHU Zhen-Gang 《Communications in Theoretical Physics》 SCIE CAS 2006年第4期761-764,共4页
We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the ... We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel Epstein model Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations. 展开更多
关键词 Turing pattern Lengyel-Epstein （LE） model
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3D Turing nanowrinkles via anisotropic photopolymerization 认领 引用
2
作者 Qi Duan Xian-Zi Dong +3 位作者 Jie Liu Fan-Chun Bin Xin-Yi Wu Mei-Ling Zheng 《International Journal of Extreme Manufacturing》 SCIE EI CAS CSCD 2026年第2期544-559,共16页
Inspired by the diverse wrinkled surface patterns in nature,micro-nano scale wrinkled surfaces have become an essential part of materials science.Nowadays,it is still a challenge to flexibly fabricate three-dimensiona... Inspired by the diverse wrinkled surface patterns in nature,micro-nano scale wrinkled surfaces have become an essential part of materials science.Nowadays,it is still a challenge to flexibly fabricate three-dimensional(3D)nanowrinkled structures with precise configuration.Herein,we introduce a reaction-diffusion-based self-organized Turing mechanism integrated with femtosecond laser direct writing(FsLDW)to achieve controlled anisotropic photopolymerization,fabricating 3D hydrogel-based biomimetic Turing nanowrinkled structures.This approach enables precise spatial modulation of wrinkle periodicity,orientation,and amplitude.Furthermore,using methacrylated hyaluronic acid(MeHA)monomers,we elucidate the mechanistic interplay between anisotropic photopolymerization and Turing-patterned nanowrinkle formation.We further propose a theoretical framework—the polarization modulation of femtosecond laser pulses enables the anisotropic photopolymerization of Turing-patterned nanowrinkles,selectively generating aligned linear(Turing-line)and vertically ordered pillar(Turing-column)structures.According to this theoretical framework,we propose the concept of the nanowrinkle parameter(Wr),alongside an empirical formula derived from two-photon polymerization(TPP)fabrication parameters to predict Turing nanowrinkle emergence conditions.We also demonstrate the ability to create high-resolution,3D nanowrinkled structures,including patterned structures,bio-inspired microvilli resembling those of the small intestine,cicada wing replicas,and moth-eye structures.Moreover,we functionalize Turing-patterned structures with magnetron-sputtered Ag coatings,creating microano-devices for molecular surface enhanced Raman scattering(SERS)detection.The Turing-inspired SERS devices demonstrate ultra-trace detection capability for Rhodamine 6G(R6G)at concentrations as low as 10−9M.This work provides a novel,high-precision methodology for the fabrication of complex,bionic,free-form Turing nanowrinkled structures. 展开更多
关键词 hyaluronic acid derivative two-photon polymerization 3D Turing patterns nanowrinkled structure surface-enhanced Raman scattering
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TURING PATTERNS OF A PREDATOR-PREY MODEL WITH A MODIFIED LESLIE-GOWER TERM AND CROSS-DIFFUSIONS 认领 引用 被引量：5
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作者 GUANG-PING HU XIAO-LING LI 《International Journal of Biomathematics》 SCIE 2012年第6期203-219,共17页
In this paper,a strongly coupled diffusive predator-prey system with a modified Leslie-Gower term is considered.We will show that under certain hypotheses,even though the unique positive equilibrium is asymptotically ... In this paper,a strongly coupled diffusive predator-prey system with a modified Leslie-Gower term is considered.We will show that under certain hypotheses,even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion,Turing instability can produce due to the presence of the cross-diffusion.In particular,we establish the existence of non-constant positive steady states of this system.The results indicate that cross-diffusion can create stationary patterns. 展开更多
关键词 Cross-diffusion Turing patterns priori estimates non-constant positivesteady state.
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CROSS-DIFFUSION INDUCED TURING PATTERNS IN A SEX-STRUCTURED PREDATOR-PREY MODEL 认领 引用 被引量：2
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作者 JIA LIU HUA ZHOU LAI ZHANG 《International Journal of Biomathematics》 SCIE 2012年第4期39-61,共23页
In this paper, we consider a sex-structured predator prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray Schauder degree theory, the existence and stability of both h... In this paper, we consider a sex-structured predator prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of Turing patterns are derived. 展开更多
关键词 Predator-prey model cross-diffusion turing pattern sex structure.
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Study of Turing patterns in a SI reaction-diffusion propagation system based on network and non-network environments 认领 引用 被引量：1
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作者 Yuxuan Tang Shuling Shen Linhe Zhu 《International Journal of Biomathematics》 SCIE 2024年第1期199-225,共27页
The study of rumor propagation dynamics is of great significance to reduce.false news and ensure the authenticity of news information.In this paper,a SI reaction-diffusion rumor propagation model with nonlinear satura... The study of rumor propagation dynamics is of great significance to reduce.false news and ensure the authenticity of news information.In this paper,a SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied.First,through stability analysis,we obtain the conditions for the existence and local stability of the positive equilibrium point.By selecting suitable variable as the control parameter,the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained.Then,using the above theorem and multi-scale standard analysis,the expression of amplitude equation around Turing bifurcation point is obtained.By analyzing the amplitude equation,different types of Turing pattern are divided such as uniform steady-state mode,hexagonal mode,stripe mode and mixed structure mode.Further,in the numerical simulation part,by observing different patterns corresponding to different values of control variable,the correctness of the theory is verified.Finally,the effects of different network structures on patterns are investigated.The results show that there are significant differences in the distribution of users on different network structures. 展开更多
关键词 Reaction-diffusion system rumor propagation amplitude equation Turing pattern
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Enhanced slag resistance of Al2O3-MgO refractory castable:role of CeO2 in radical-involved corrosion 认领 引用 被引量：1
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作者 Fanbo Zeng Jianghao Zhou +4 位作者 Shenghao Li Ao Huang Zhengyang Zhao Lvping Fu Huazhi Gu 《Journal of Rare Earths》 SCIE EI CAS CSCD 2026年第6期1946-1955,I0009,共10页
The presence of highly reactive species such as superoxide radicals in the CaO-Al2O3-SiO2 slag induces the formation of Turing pattern corrosion at the reaction interface between Al2O3-MgO refractory ca... The presence of highly reactive species such as superoxide radicals in the CaO-Al2O3-SiO2 slag induces the formation of Turing pattern corrosion at the reaction interface between Al2O3-MgO refractory castable and slag.This phenomenon can significantly accelerate the corrosion rate of refractories.The potential of CeO2 to inhibit radical reactions between slag and refractory has been identified as a promising avenue for corrosion inhibition.In this study,the microstructural evolution and slag resistance of Al2O3-MgO refractory castables with the addition of CeO2 were investigated.The results reveal that under high-tempe rature conditions,CeO2 undergoes solid-solution transfo rmation into the CA6 and MgAl2O4 phases within the refractory and maintains a high oxidation state(Ce4+),and it possesses the ability to scavenge superoxide radicals.And the dissolved Ce4+has the capacity to reduce the superoxide radical content of slag.Therefore,the addition of 0.5 wt%CeO2 leads to a substantial reduction in both the height of the interface Turing pattern corrosion peak and the corrosion index by 21.94%and41.27%,respectively.However,th e addition of CeO2 in excess of 0.75 wt%leads to increased lattice distortion in MgAl2O4 and reduced crystallinity,resulting in diminished sintering properties and increased apparent porosity(up to 25.54%).Furthermore,the dissolution of Ce4+leads to a substantial decrease in the slag polymerization degree,while concurrently promoting the generation of superoxide radicals within the slag,thereby resulting in the intensification of the Turing pattern corrosion phenomenon.This study provides a theoretical foundation for the development of refractories for highquality steel refining. 展开更多
关键词 Al₂O₃-MgO refractory castable Rare earths Turing pattern corrosion Three-phase interface High-temperature radical reaction
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Spatiotemporal heterogeneity of a network epidemic model with higher-order interactions and advection mechanisms 认领 引用
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作者 Wenlong Zhang Xuerui Zhu Linhe Zhu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2026年第6期163-184,共22页
Reaction-diffusion infectious disease models are widely used to describe the spatial distribution of infected individuals.In this study,we construct network-based reaction-diffusion models that incorporate both higher... Reaction-diffusion infectious disease models are widely used to describe the spatial distribution of infected individuals.In this study,we construct network-based reaction-diffusion models that incorporate both higher-order interactions and advection mechanisms,formulated on a triangular lattice torus network.This idealized structure is adopted to facilitate explicit derivation and linear stability analysis of the theoretical conditions for Turing instability—analyses that would be considerably more challenging in complex heterogeneous geometries.To address the computational challenge of generating higher-order node Laplacian matrices in large-scale networks,we develop a dimensionality reduction strategy using graph-structured edge Laplacians.The theoretical analysis reveals how higher-order interactions and advection jointly influence the onset of Turing patterns.Furthermore,model fitting to real epidemic datausing a mobility network constructed from 2020 inter-prefectural commuting flows across Japan's 47 prefectures—shows that incorporating higher-order interactions results in better fitting performance compared to conventional models. 展开更多
关键词 higher-order interaction advection mechanism network epidemic Turing pattern physics-informed neural networks
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Spatial patterns of the Brusselator model with asymmetric Lévy diffusion 认领 引用
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作者 Hongwei Yin Shangtao Yang +2 位作者 Xiaoqing Wen Haohua Wang Shufen Yang 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第11期129-136,共8页
The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such ... The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such as normal or fractional Laplace diffusion),namely,assuming that spatial environments of the systems are homogeneous.However,the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants.Naturally,there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems.To answer this,we build a general asymmetric L´evy diffusion model based on the theory of a continuous time random walk.In addition,we investigate the two-species Brusselator model with asymmetric L´evy diffusion,and obtain a general condition for the formation of Turing and wave patterns.More interestingly,we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters,the asymmetry of L´evy diffusion for this model can produce wave patterns.This is different from the previous result that wave instability requires at least a three-species model.In addition,the asymmetry of L´evy diffusion can significantly affect the amplitude and frequency of the spatial patterns.Our results enrich our knowledge of the mechanisms of pattern formation. 展开更多
关键词 asymmetric Lévy diffusion Turing and wave patterns Brusselator model
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Turing pattern engineering enables kinetically ultrastable yet ductile metallic glasses 认领 引用
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作者 Huanrong Liu Qingan Li +3 位作者 Shan Zhang Rui Su Yunjiang Wang Pengfei Guan 《Materials Futures》 EI CSCD 2026年第2期179-193,共15页
Enhancing the kinetic stability of glasses typically requires deepening their thermodynamic stability,which increases structural rigidity and degrades ductility;decoupling these properties remains a major challenge.He... Enhancing the kinetic stability of glasses typically requires deepening their thermodynamic stability,which increases structural rigidity and degrades ductility;decoupling these properties remains a major challenge.Here,we demonstrate that spatial patterning in metallic glasses produces exceptional kinetic ultrastability that coexists with a thermodynamically metastable,high-energy state and excellent plasticity.Guided by atomistic simulations using replica exchange molecular dynamics and machine learning interatomic potentials,we reveal that oxygen,through reaction-diffusion-coupled pattern dynamics,self-organizes into oxygen-centered pinned structures(OPSs)that serve as localized kinetic constraints.These motifs drastically slow structural relaxation,delivering kinetic stability comparable to ultrastable glasses even as the system retains the high inherent energy of rapidly quenched states.The OPSs’topology yields a spatially uniform activation of plastic events,promoting strain delocalization under mechanical load.By geometrically tailoring oxygen patterns,we increase the glass transition onset temperature(Tonset)by about 200 K with negligible loss of deformability.Our findings establish a practicable paradigm for decoupling kinetic and thermodynamic stability and point to a scalable,additive route for designing amorphous materials that combine hyperstability with plasticity. 展开更多
关键词 metallic glasses kinetic stability Turing pattern reaction-diffusion model
Patterns dynamics in a diffusive prey-predator system with ratio-dependent functional response in a planar domain 认领 引用
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作者 Xiang-Ping Yan Cun-Hua Zhang 《International Journal of Biomathematics》 SCIE 2025年第6期139-162,共24页
This paper is concerned with a classical two-species prey-predator reaction-diffusion system with ratio-dependent functional response and subject to homogeneous Neumann boundary condition in a two-dimensional rectangl... This paper is concerned with a classical two-species prey-predator reaction-diffusion system with ratio-dependent functional response and subject to homogeneous Neumann boundary condition in a two-dimensional rectangle domain.By analyzing the associated eigenvalue problem,the spatially homogeneous Hopf bifurcation curve and Turing bifurcation curve of system at the constant coexistence equilibrium are established.Then when the bifurcation parameter is in the interior of range for Turing instability and near Turing bifurcation curve,the amplitude equations of the original system near the constant coexistence equilibrium are obtained by multiple-scale time perturbation analysis.On the basis of the obtained amplitude equations,the stability and classifications of spatiotemporal patterns of the original system at the constant coexistence equilibrium are discussed.Finally,to verify the validity of the obtained theoretical results,numerical simulations are also carried out. 展开更多
关键词 Prey-predator reaction-diffusion system amplitude equations Turing pattern
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Radical-reaction driving nonlinear corrosion behavior and inhibition mechanism of Ce3+/Ce4+redox couple on molten slag/refractory interface 认领 引用 被引量：1
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作者 Fanbo Zeng Xinlian Wang +5 位作者 Shenghao Li Ao Huang Shiqiang Wang Yongshun Zou Lvping Fu Huazhi Gu 《Corrosion Communications》 EI CSCD 2026年第1期26-36,共11页
A novel nonlinear corrosion at the three-phase interface of corundum refractory with CaO-Al2O3-SiO2slag was identified as a Turing pattern phenomenon caused by auto-catalytic reactions involving free radicals... A novel nonlinear corrosion at the three-phase interface of corundum refractory with CaO-Al2O3-SiO2slag was identified as a Turing pattern phenomenon caused by auto-catalytic reactions involving free radicals Ca+and O22-.The differences in diffusion rate between Ca+and O22-result in an unstable distribution of products at each reaction site,leading to nonlinear dynamic reactions with a periodic corrosion pattern.Efficiency of the interfacial auto-catalytic reaction was inhibited by the radical quenching effect of the Ce3+/Ce4+redox couple modified on the surface of corundum refractory,resulting in complete suppression of the Turing pattern formation. 展开更多
关键词 Molten slag Refractory Nonlinear corrosion Radical reaction Turing pattern Ce3+/Ce4+quenching effect
Stability switches mechanism and PID control in reaction-diffusion network-organized neural systems with transmission delays 认领 引用 被引量：2
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作者 Xiangyu DU Min XIAO +1 位作者 Wenwu YU Jiajin HE 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2025年第2期199-215,共17页
Traditionally,the spatiotemporal dynamics of neural networks have been analyzed in the locally continuous domain.While this modeling approach is straightforward and practical,it fails to encapsulate real-world network... Traditionally,the spatiotemporal dynamics of neural networks have been analyzed in the locally continuous domain.While this modeling approach is straightforward and practical,it fails to encapsulate real-world networks’intricate topological structures and evolution.Currently,the mechanisms of stability switches induced by time delays and diffusion effects in networkorganized systems are still vague.Besides,effective dynamic optimization strategies for network-organized models remain to be devised.In this study,we develop a delayed reaction-diffusion neural network model on complex networks.This system incorporates the effects of inter-nodal diffusion coupling and exhibits profound architectural complexity.We then pioneer the proportional-integral-derivative(PID)feedback control into the network-organized model to modulate dynamic behaviors.The linear stability analysis is conducted firstly,demonstrating that Turing patterns and Hopf bifurcation can be induced in the controlled neural network by varying diffusion coefficients and time delays.Subsequently,the bifurcation direction is deduced via the center manifold theorem.Finally,a series of simulations are performed to validate the theoretical analysis and substantiate the efficacy of the PID control strategy.The results exhibit that the PID feedback controller can flexibly regulate the dynamics of the network-organized systems and possesses excellent disturbance rejection capabilities. 展开更多
关键词 complex network neural networks PID control turing instability hopf bifurcation time delays turing pattern
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Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations:Pattern Formation Under Uniform Differential Advection 认领 引用
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作者 S.G.Ayodele D.Raabe F.Varnik 《Communications in Computational Physics》 SCIE 2013年第3期741-756,共16页
A lattice Boltzmann model for the study of advection-diffusion-reaction(ADR)problems is proposed.Via multiscale expansion analysis,we derive from the LB model the resulting macroscopic equations.It is shown that a lin... A lattice Boltzmann model for the study of advection-diffusion-reaction(ADR)problems is proposed.Via multiscale expansion analysis,we derive from the LB model the resulting macroscopic equations.It is shown that a linear equilibrium distribution is sufficient to produce ADR equations within error terms of the order of the Mach number squared.Furthermore,we study spatially varying structures arising from the interaction of advective transport with a cubic autocatalytic reaction-diffusion process under an imposed uniform flow.While advecting all the present species leads to trivial translation of the Turing patterns,differential advection leads to flow induced instability characterized with traveling stripes with a velocity dependent wave vector parallel to the flow direction.Predictions from a linear stability analysis of the model equations are found to be in line with these observations. 展开更多
关键词 Advective transport differential advection Turing patterns linear stability lattice Boltzmann
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