Bifurcations of nontwisted heteroclinic loop

被引：18

作者：

Tian, QP ^{[1
]}

Zhu, DM ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY | 2000年 / 43卷 / 08期

基金：

中国国家自然科学基金;

关键词：

heteroclinic orbit; homoclinic orbit; periodic orbit; inside stability;

D O I：

10.1007/BF02884181

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Bifurcations of nontwisted and fine heteroclinic loops are studied for higher dimensional systems. The existence and its associated existing regions are given for the 1-hom orbit and the 1-per orbit, respectively, and bifurcation surfaces of the two-fold periodic orbit are also obtained. At last, these bifurcation results are applied to the fine heteroclinic loop for the planar system, which leads to some new and interesting results.

引用

页码：818 / 828

页数：11

共 13 条

[1] EXPONENTIAL DICHOTOMIES, HETEROCLINIC ORBITS, AND MELNIKOV FUNCTIONS
BATTELLI, F
LAZZARI, C
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 86 (02) : 342 - 366
[2] Chow S-N., 1991, APPL ANAL, V42, P275
[3] THE BIFURCATION OF HOMOCLINIC AND PERIODIC-ORBITS FROM 2 HETEROCLINIC ORBITS
CHOW, SN
DENG, B
TERMAN, D
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1990, 21 (01) : 179 - 204
[4] FENG B, 1991, SCI CHINA SER A, V21, P673
[5] Han M., 1992, Acta Mech. Sin. (Beijing), V35, P673
[6] Kokubu H., 1988, JAPAN J APPL MATH, V5, P455, DOI [10.1007/BF03167912, DOI 10.1007/BF03167912]
[7] DEGENERATE AND NONTRIVIAL HYPERBOLIC POLYCYCLES WITH 2 VERTICES
MOURTADA, A
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 113 (01) : 68 - 83
[8] Reyn J. W., 1980, LECT NOTES MATH, V810, P264
[9] Zhu D, 1997, Nonlinear Analysis TMA, V28, P547
[10] Zhu D., 1998, J E CHINA NORMAL U, P19

← 1 2 →