USING MELNIKOV METHOD TO SOLVE SILNIKOV PROBLEMS

被引：150

作者：

LIN, XB

机构：

[1] Department of Mathematics, North Carolina State University, Raleigh

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 1990年 / 116卷

关键词：

D O I：

10.1017/S0308210500031528

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite. Examples include generalisations of Silnikov's main theorems and a retreatment of a singularly perturbed delay differential equation.

引用

页码：295 / 325

页数：31

共 29 条

[1] BIFURCATION FROM A HOMOCLINIC ORBIT IN PARABOLIC DIFFERENTIAL-EQUATIONS [J].

BLAZQUEZ, CM .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1986, 103 :265-274

[2]

Bohr H., 1951, ALMOST PERIODIC FUNC

[3]

Chow S., 1989, J DYNAM DIFF EQU, V1, P3, DOI DOI 10.1007/BF01048789)

[4] AN EXAMPLE OF BIFURCATION TO HOMOCLINIC ORBITS [J].

CHOW, SN ;

HALE, JK ;

MALLETPARET, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1980, 37 (03) :351-373

[5]

CHOW SN, HOMOCLINIC HETEROCLI

[6]

CHOW SN, HOMOCLINIC BIFURCATI

[7]

CHOW SN, IN PRESS SIAM J APP

[8]

CHOW SN, BIFURCATION HOMOCLIN

[9]

GUCKENHEIMER J, 1986, APPLIED MATH SCI, V42

[10]

HALE J, 1977, THEORY FUNCTIONAL DI

← 1 2 3 →