The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a...The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a subharmonic solution are obtained.展开更多
The existence conditions of an invariant torus for general planar periodic perturbed systems are given.It is proved that the perturbed systems may have not only large invariant tori which appear in pair,but also small...The existence conditions of an invariant torus for general planar periodic perturbed systems are given.It is proved that the perturbed systems may have not only large invariant tori which appear in pair,but also small invariant tori.展开更多
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
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
CONSIDER the following equation: （?）=f（x）+f<sub>1</sub>（x,λ）+f<sub>2</sub>（t,x,μ）, （1） where λ, μ are real scalar parameters; f, f<sub>1</sub> and f<sub>2</su...CONSIDER the following equation: （?）=f（x）+f<sub>1</sub>（x,λ）+f<sub>2</sub>（t,x,μ）, （1） where λ, μ are real scalar parameters; f, f<sub>1</sub> and f<sub>2</sub> are C<sup>3</sup> functions in their variables, and f<sub>1</sub>（x, 0）=0, f<sub>2</sub>（t, x, 0）=0, f<sub>2</sub>（t+2π, x, μ）=f+2（t, x, μ）. Suppose that for λ=μ=0, eq. （1） has a semistable limit cycle L of multiple two. The problem is to discuss展开更多
Consider the time-periodic perturbations of an n-dimensional autonomous system with a nonhyperbolic closed orbit in the phase space. By the method of averaging and Floquet theory, the bifurcations of the invariant tor...Consider the time-periodic perturbations of an n-dimensional autonomous system with a nonhyperbolic closed orbit in the phase space. By the method of averaging and Floquet theory, the bifurcations of the invariant torus in the extended phase space are studied.展开更多
基金Progect supported by the National Natural Science Foundation of China.
文摘The time-periodic perturbations of planar Hamiltonian systems are investigated.A necessary condition for the existence of an invariant torus,a sufficient condition for the bifurcation of a unique invariant torus and a subharmonic solution are obtained.
基金Project supported by the National Natural Science Foundation of China.
文摘The existence conditions of an invariant torus for general planar periodic perturbed systems are given.It is proved that the perturbed systems may have not only large invariant tori which appear in pair,but also small invariant tori.
文摘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.
基金Project supported by the National Natural Science Foundation of China (No. 10671214)the Chongqing Natural Science Foundation of China (No. 2005cc14)Shanghai Shuguang Genzong Project (No.04SGG05)
文摘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.
文摘CONSIDER the following equation: （?）=f（x）+f<sub>1</sub>（x,λ）+f<sub>2</sub>（t,x,μ）, （1） where λ, μ are real scalar parameters; f, f<sub>1</sub> and f<sub>2</sub> are C<sup>3</sup> functions in their variables, and f<sub>1</sub>（x, 0）=0, f<sub>2</sub>（t, x, 0）=0, f<sub>2</sub>（t+2π, x, μ）=f+2（t, x, μ）. Suppose that for λ=μ=0, eq. （1） has a semistable limit cycle L of multiple two. The problem is to discuss
基金Project supported by the National Natural Science Foundation of Chinathe Foundation for University Key Teacher by the Ministry.
文摘Consider the time-periodic perturbations of an n-dimensional autonomous system with a nonhyperbolic closed orbit in the phase space. By the method of averaging and Floquet theory, the bifurcations of the invariant torus in the extended phase space are studied.
