In this paper, the Melnikov function method has been used to analyse the distance between stable manifold and unstable manifold of the soft spring Duffing equation([1]) after its heteroclinic orbits rupture as the res...In this paper, the Melnikov function method has been used to analyse the distance between stable manifold and unstable manifold of the soft spring Duffing equation([1]) after its heteroclinic orbits rupture as the result of a small perturbation. The conditions that limit circles are bifurcated are given, and then their stability and location is determined.展开更多
In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cy...In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cycle. We improve some important results.展开更多
In this paper, we use the Melnikov function method to study a kind of soft Duffing equations[1] and give the condition that the equations have chaotic motion and bifurcation. The method used in this paper is effective...In this paper, we use the Melnikov function method to study a kind of soft Duffing equations[1] and give the condition that the equations have chaotic motion and bifurcation. The method used in this paper is effective for dealing with the Melnikov function integral of the system whose explict expression of the homoclinic or heteroclinic orbit cannot be given.展开更多
The dynamics behavior of tension bar with periodic tension velocity was presented. Melnikov method war used to study the dynamic system. The results show that material nonlinear may result in anomalous dynamics respon...The dynamics behavior of tension bar with periodic tension velocity was presented. Melnikov method war used to study the dynamic system. The results show that material nonlinear may result in anomalous dynamics response. The subharmonic bifurcation and chaos may occur in the determined system when the tension velocity exceeds the critical value.展开更多
In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic l...In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.展开更多
Using the method of multi-parameter perturbation theory and qualitative analysis,a cubic system perturbed by degree four are investigated in this paper. After systematic analysis,it is found that the studied system ca...Using the method of multi-parameter perturbation theory and qualitative analysis,a cubic system perturbed by degree four are investigated in this paper. After systematic analysis,it is found that the studied system can have nine limit cycles with their distributions are obtained.展开更多
文摘In this paper, the Melnikov function method has been used to analyse the distance between stable manifold and unstable manifold of the soft spring Duffing equation([1]) after its heteroclinic orbits rupture as the result of a small perturbation. The conditions that limit circles are bifurcated are given, and then their stability and location is determined.
文摘In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cycle. We improve some important results.
文摘In this paper, we use the Melnikov function method to study a kind of soft Duffing equations[1] and give the condition that the equations have chaotic motion and bifurcation. The method used in this paper is effective for dealing with the Melnikov function integral of the system whose explict expression of the homoclinic or heteroclinic orbit cannot be given.
文摘The dynamics behavior of tension bar with periodic tension velocity was presented. Melnikov method war used to study the dynamic system. The results show that material nonlinear may result in anomalous dynamics response. The subharmonic bifurcation and chaos may occur in the determined system when the tension velocity exceeds the critical value.
基金supported by the National Natural Science Foundation of China(No.11271261)the Natural Science Foundation of Anhui Province(No.1308085MA08)the Doctoral Program Foundation(2012)of Anhui Normal University
文摘In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.
基金supported by the Natural Science Foundation of Shandong Province,China（No.ZR2010AZ003）
文摘Using the method of multi-parameter perturbation theory and qualitative analysis,a cubic system perturbed by degree four are investigated in this paper. After systematic analysis,it is found that the studied system can have nine limit cycles with their distributions are obtained.
