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
Bifurcation problems of high dimensional system with several parameters are considered. Assume that the system has an invariant manifold, which consists entirely of periodic orbits and has a center subspace with two d...Bifurcation problems of high dimensional system with several parameters are considered. Assume that the system has an invariant manifold, which consists entirely of periodic orbits and has a center subspace with two dimensions in nor mal direction. The existence and the normal hyperbolicity of the 2-dimensional invariant torus and the 3-dimensional invariant torus are given. The phenome non of bifurcation for the 3-dimensional invariant torus from one single periodic orbit is discovered for the first time.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
We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian pert...We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for application, we prove that a finite network of Duffing oscillators with periodic external forces possesses Lagrange stability for almost all initial data.展开更多
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.
文摘Bifurcation problems of high dimensional system with several parameters are considered. Assume that the system has an invariant manifold, which consists entirely of periodic orbits and has a center subspace with two dimensions in nor mal direction. The existence and the normal hyperbolicity of the 2-dimensional invariant torus and the 3-dimensional invariant torus are given. The phenome non of bifurcation for the 3-dimensional invariant torus from one single periodic orbit is discovered for the first time.
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.
基金supported by National Natural Science Foundation of China(Grant No.12071254)。
文摘We prove that there is an invariant torus with the given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for application, we prove that a finite network of Duffing oscillators with periodic external forces possesses Lagrange stability for almost all initial data.
