期刊文献+
共找到13篇文章
< 1 >
每页显示 20 50 100
ON THE COEFFICIENTS APPEARING IN THE EXPANSION OF MELNIKOV FUNCTIONS IN HOMOCLINIC BIFURCATIONS 被引量:4
1
作者 韩茂安 叶彦谦 《Annals of Differential Equations》 1998年第2期58-64,共7页
We give computing formulas for the first three coefficients appearing in the expansion of the Melnikov function in homoclinic bifurcations.
关键词 homoclinic bifurcation Melnikov function
原文传递
WHAT ARE THE SEPARATRIX VALUES NAMED BY LEONTOVICH ON HOMOCLINIC BIFURCATION 被引量:1
2
作者 骆海英 李继彬 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第4期457-464,共8页
For a given system, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of the third separatrix values named by Leontovich for the multi... For a given system, by using the Tkachev method which concerned with the proof of the stability of a multiple limit cycle, the exact computation formula of the third separatrix values named by Leontovich for the multiple limit cycle bifurcation was given, which was one of the main criterions for the number of limit cycles bifurcated from a homoclinic orbit and the stability of the homoclinic loop, and a computation formula for higher separatrix values was conjectured. 展开更多
关键词 homoclinic bifurcation separatrix value saddle value limit cycle
下载PDF
Problems in Homoclinic Bifurcation with Higher Dimensions 被引量:31
3
作者 Zhu Deming Department of Mathematics, East China Normal University. Shanghai 200062. China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1998年第3期341-352,共12页
In this paper, a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincare map is established ... In this paper, a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincare map is established to solve various problems in homoclinic bifurcations with codimension one or two. Bifurcation diagrams and bifurcation curves are given. 展开更多
关键词 Exponential dichotomy Local coordinates homoclinic bifurcation Periodic orbit
原文传递
Stability and Uniqueness of Periodic Orbits Produced During Homoclinic Bifurcation 被引量:8
4
作者 Zhu Deming 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1995年第3期267-277,共11页
Under a generic assumption, the existence and the uniqueness of the periodic orbit generating from a homoclinic bifurcation are shown, and the dimensions of its stable and unstable manifolds are given. In the case of ... Under a generic assumption, the existence and the uniqueness of the periodic orbit generating from a homoclinic bifurcation are shown, and the dimensions of its stable and unstable manifolds are given. In the case of a 3-dimensional system, our result revises the stability criterion given in [4,5]. 展开更多
关键词 homoclinic bifurcation Periodic orbit Stable manifolds DIMENSIONS
原文传递
Analysis of chaos behaviors of a bistable piezoelectric cantilever power generation system by the second-order Melnikov function 被引量:5
5
作者 Shu Sun Shu-Qian Cao 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2017年第1期200-207,共8页
By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by ... By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given. 展开更多
关键词 Bistable piezoelectric cantilever beam Second order Melnikov function homoclinic bifurcation Basin of attraction
下载PDF
HOMOCLINIC BIFURCATION WITH CODIMENSION 3 被引量:5
6
作者 ZHU DEMING(Department of Matehematics,East China Normal University, Shanghai 200062, China) 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1994年第2期205-216,共12页
First it is proved that both the integral of the divergence and the Melnikov function are invariants of the C2 transformation. Then, the problem of the planar homoclinic bifurcation with codimension 3 is considered. I... First it is proved that both the integral of the divergence and the Melnikov function are invariants of the C2 transformation. Then, the problem of the planar homoclinic bifurcation with codimension 3 is considered. It is proved that, in a small neighborhood of the origin in the parameter space of a Cr (r≥5) system, there exist exactly two Cr-1 semi- stable- limit- cycle branching surfaces, and their common boundary is a unique Cr-1 three-multiple- limit-cycle branching curve. The bifurcation pictures and the asymptotic expansions of the bifurcation functions are given. The stability criterion for the homoclinic loop is also obtained when the integral of the divergence is zero. The proof of the auxiliary theorems will be presented in [16]. 展开更多
关键词 homoclinic bifurcation CODIMENSION Semi-stable-limit-cycle branch Three- multiple-limit- cycle branch.
原文传递
Bifurcation and Chaotic Dynamics of Homoclinic Systems in R^3 被引量:2
7
作者 Sun Jianhua Department of Mathematics Nanjing University Nanjing, 210008 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1995年第2期128-136,共9页
We consider perturbations which may or may not depend explicitly on time for the three-dimensional homoclinic systems. We obtain the existence and bifurcation theorems for transversal homoclinic points and homoclinic ... We consider perturbations which may or may not depend explicitly on time for the three-dimensional homoclinic systems. We obtain the existence and bifurcation theorems for transversal homoclinic points and homoclinic orbits, and illustrate our results with two examples. 展开更多
关键词 bifurcation and Chaotic Dynamics of homoclinic Systems in R~3
原文传递
HOMOCLINIC BIFURCATION IN SEMI-CONTINUOUS DYNAMIC SYSTEMS 被引量:3
8
作者 CHUANJUN DAI MIN ZHAO LANSUN CHEN 《International Journal of Biomathematics》 2012年第6期183-201,共19页
In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields... In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results. 展开更多
关键词 Rotated vector fields homoclinic cycle homoclinic bifurcation order-1 cycle semi-continuous.
原文传递
On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z_3 Invariant Quintic Perturbations
9
作者 Yu Hal WU Mao An HAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第5期869-878,共10页
A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered. By applying the qualitative method of differential equations and the numeric computing method, the Hopf bifurca... A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered. By applying the qualitative method of differential equations and the numeric computing method, the Hopf bifurcation, homoclinic loop bifurcation and heteroclinic loop bifurcation of the above perturbed system are studied. It is found that the above system has at least 12 limit cycles and the distributions of limit cycles are also given. 展开更多
关键词 homoclinic loop bifurcation heteroclinic loop bifurcation Hopf bifurcation stability limit cycles
原文传递
Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions
10
作者 Ran Chao WU Jian Hua SUN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第6期1651-1656,共6页
Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are studied. By establishing a local coordinate system and a Poincare map near the homoclinic orbit, the existence and uniquenes... Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are studied. By establishing a local coordinate system and a Poincare map near the homoclinic orbit, the existence and uniqueness of 1-homoclinic orbit and 1-periodic orbit are given. Also considered is the existence of 2-homoclinic orbit and 2-periodic orbit. In additon, the corresponding bifurcation surfaces are given. 展开更多
关键词 Orbit flip homoclinic bifurcations Poincaré map
原文传递
Microbial insecticide model and homoclinic bifurcation of impulsive control system
11
作者 Tieying Wang 《International Journal of Biomathematics》 SCIE 2021年第6期173-187,共15页
A new microbial insecticide mathematical model with density dependent for pest is proposed in this paper.First,the system without impulsive state feedback control is considered.The existence and stability of equilibri... A new microbial insecticide mathematical model with density dependent for pest is proposed in this paper.First,the system without impulsive state feedback control is considered.The existence and stability of equilibria are investigated and the properties of equilibria under different conditions are verified by using numerical simulation.Since the system without pulse has two positive equilibria under some additional assumptions,the system is not globally asymptotically stable.Based on the stability analysis of equilibria,limit cycle,outer boundary line and Sotomayor's theorem,the existence of saddle-node bifurcation and global dynamics of the system are obtained.Second,we consider homoclinic bifurcation of the system with impulsive state feedback control.The existence of order-1 homoclinic orbit of the system is studied.When the impulsive function is slightly disturbed,the homoclinic orbit breaks and bifurcates order-1 periodic solution.The existence and stability of order-1 periodic solution are obtained by means of theory of semi-continuous dynamic system. 展开更多
关键词 Mathematical model of microbial insecticide state feedback control system homoclinic orbit homoclinic bifurcation.
原文传递
Analysis of a Shil’nikov Type Homoclinic Bifurcation
12
作者 Yan Cong XU Xing Bo LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第5期901-910,共10页
The bifurcation associated with a homoclinic orbit to saddle-focus including a pair of pure imaginary eigenvalues is investigated by using related homoclinie bifurcation theory. It is proved that, in a neighborhood of... The bifurcation associated with a homoclinic orbit to saddle-focus including a pair of pure imaginary eigenvalues is investigated by using related homoclinie bifurcation theory. It is proved that, in a neighborhood of the homoclinic bifurcation value, there are countably infinite saddle-node bifurcation values, period-doubling bifurcation values and double-pulse homoclinic bifurcation values. Also, accompanied by the Hopf bifurcation, the existence of certain homoclinie connections to the periodic orbit is proved. 展开更多
关键词 homoclinic bifurcation Hopf bifurcation Poincare map
原文传递
Perturbations from a kind of quartic Hamiltonians under general cubic polynomials 被引量:2
13
作者 ZHAO LiQin WANG Qi 《Science China Mathematics》 SCIE 2009年第3期427-442,共16页
In this paper we investigate the perturbations from a kind of quartic Hamiltonians under general cubic polynomials. It is proved that the number of isolated zeros of the related abelian integrals around only one cente... In this paper we investigate the perturbations from a kind of quartic Hamiltonians under general cubic polynomials. It is proved that the number of isolated zeros of the related abelian integrals around only one center is not more than 12 except the case of global center. It is also proved that there exists a cubic polynomial such that the disturbed vector field has at least 3 limit cycles while the corresponding vector field without perturbations belongs to the saddle loop case. 展开更多
关键词 abelian integral elliptic Hamiltonian homoclinic bifurcation 58F14 58F21 58F30 34C05
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部