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BIFURCATIONS OF SUBHARMONIC SOLUTIONS IN PERIODIC PERTURBATION OF A HYPERBOLIC LIMIT CYCLE 认领 引用 被引量：1
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作者 HAN Mao-an +1 位作者 GU Sheng-shi 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第8期981-986,共6页
Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for th... Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained. An example is given in the end of the paper. 展开更多
关键词 bifurcation subharmonic solution limit cycle
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1/3 SUBHARMONIC SOLUTION OF ELLIPTICAL SANDWICH PLATES 认领 引用
2
作者 李银山 张年梅 杨桂通 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第10期1147-1157,共11页
The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elli... The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected. 展开更多
关键词 elliptical sandwich plate superpositive-iterative harmonic balance (SIHB) method 1/3 subharmonic solution bifurcation
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Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System 认领 引用 被引量：4
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作者 Zhiyong YE Maoan HAN 《Chinese Annals of Mathematics,Series B》 SCIE 2007年第2期135-148,共14页
This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-... This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied. 展开更多
关键词 Singular perturbation Subharmonic solution Saddle-Node Invariant torus
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Brake subharmonic solutions of first order Hamiltonian systems 认领 引用 被引量：6
4
作者 LI Chong LIU ChunGen 《Science China Mathematics》 SCIE 2010年第10期2719-2732,共14页
In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous ... In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian systems.We prove that when the positive integers j and k satisfy the certain conditions,there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct. 展开更多
关键词 brake subharmonic solution L-Maslov type index Hamiltonian systems
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Brake Subharmonic Solutions of Subquadratic Hamiltonian Systems 认领 引用 被引量：5
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作者 Chong LI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第3期405-418,共14页
The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z（t） = JVH... The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z（t） = JVH（t, z（t））, where H（t, z） = 1/2（B（t）z, z） ＋ H（t, z）, B（t） is a semipositive symmetric continuous matrix and H is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct. 展开更多
关键词 Brake subharmonic solution L-Maslov type index Hamiltonian systems
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Periodic Orbits and Invariant Tori from a Semistable Limit Cycle in the Fast Dynamics 认领 引用
6
作者 叶志勇 韩茂安 《Journal of Shanghai Jiaotong university(Science)》 EI 2006年第1期107-112,共6页
Some global behavior for a slowly varying oscillator was investigated. Based on a series of transformations and the theory of periodic orbits and integral manifold, the bifurcations of subharmonic solutions and invari... Some global behavior for a slowly varying oscillator was investigated. Based on a series of transformations and the theory of periodic orbits and integral manifold, the bifurcations of subharmonic solutions and invariant tori generated from a semistable limit cycle in the fast dynamics were discussed. 展开更多
关键词 singular perturbation subharmonic solution invariant torus
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BOUNDEDNESS OF SOLUTIONS FOR SUPERLINEAR REVERSIBLE SYSTEMS 认领 引用
7
作者 LI XIONG 《Chinese Annals of Mathematics,Series B》 SCIE 2001年第1期31-46,共16页
This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in ... This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions. 展开更多
关键词 Boundedness of solutions Quasiperiodic solutions Subharmonic solutions KAM theory Reversible systems
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Periodic perturbation of planar systems with a semistable limit cycle 认领 引用 被引量：1
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作者 HAN Mao’an 《Chinese Science Bulletin》 1997年第4期265-270,共6页
CONSIDER the following equation:x=f(x)+f(x,λ)+f2(t,x,pμ),(1)whereλ,fr are real scalar parameters;f,fi and f2 are Cfunctions in their variables,and f(d.0)=0,f(t,x,0)=0,f2(t+2π,r,μ)=f2(t,x,μ).Suppose that forλ=μ... CONSIDER the following equation:x=f(x)+f(x,λ)+f2(t,x,pμ),(1)whereλ,fr are real scalar parameters;f,fi and f2 are Cfunctions in their variables,and f(d.0)=0,f(t,x,0)=0,f2(t+2π,r,μ)=f2(t,x,μ).Suppose that forλ=μ=0),eq.(1)has a semistable limit cycle L of multiple two.The problem is to discuss what happens to the solution of(1)in a neighborhood W of L as(λ,μ)varies in a neighborhood of(0,0). 展开更多
关键词 limit cycle invariant torus subharmonic solution
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