FROM SINE WAVES TO SQUARE WAVES IN DELAY EQUATIONS

被引：40

作者：

CHOW, SN

HALE, JK

HUANG, W

机构：

[1] Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 1992年 / 120卷

基金：

美国国家科学基金会;

关键词：

D O I：

10.1017/S0308210500032108

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Suppose f(lambda): R --> R, f(lambda)(0) = 0, and the fixed point zero undergoes a generic supercritical period doubling bifurcation at lambda = 0. We characterise those small values of epsilon > 0, lambda is-an-element-of R for which there are periodic solutions of period approximately two of the equation epsilon-x(t) + x(t) = f(lambda)(x(t - 1)). As epsilon --> 0, these solutions approach square waves.

引用

页码：223 / 229

页数：7

共 17 条

[1]

CARR J, 1981, APPLIED MATH SCI, V35

[2]

Chow S.-N., 1986, CONT MATH, V56, P9

[3]

CHOW SN, 1986, CASP MATH, V3, P14

[4]

CHOW SN, 1983, COUPLED NONLINEAR OS

[5]

CHOW SN, 1991, SINGULAR PERTURBATIO

[6] PERTURBATION-THEORY FOR DUAL SEMIGROUPS .1. THE SUN-REFLEXIVE CASE [J].

CLEMENT, P ;

DIEKMANN, O ;

GYLLENBERG, M ;

HEIJMANS, HJAM ;

THIEME, HR .

MATHEMATISCHE ANNALEN, 1987, 277 (04) :709-725

[7]

CLEMENT P, 1989, P ROY SOC EDINB, V109, P145

[8] OBSERVATION OF CHAOS IN OPTICAL BISTABILITY [J].

GIBBS, HM ;

HOPF, FA ;

KAPLAN, DL ;

SHOEMAKER, RL .

PHYSICAL REVIEW LETTERS, 1981, 46 (07) :474-477

[9]

GLASS L, 1977, SCIENCE, V191, P287

[10]

HALE J, 1977, THEORY FUNCTIONAL DI

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