STABILITY AND BIFURCATIONS OF EQUILIBRIA IN A MULTIPLE-DELAYED DIFFERENTIAL-EQUATION

被引：159

作者：

BELAIR, J

CAMPBELL, SA

机构：

[1] UNIV MONTREAL,CTR RECH MATH,MONTREAL H3C 3J7,PQ,CANADA

[2] MCGILL UNIV,CTR NONLINEAR DYNAM PHYSIOL & MED,MONTREAL H3G 1Y6,PQ,CANADA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1994年 / 54卷 / 05期

关键词：

FUNCTIONAL DIFFERENTIAL EQUATIONS; FEEDBACK; HOPF BIFURCATIONS; NORMAL FORMS;

D O I：

10.1137/S0036139993248853

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The influence of multiple negative delayed feedback loops on the stability of a single-action mechanism are considered. A characteristic equation for the linearized stability of the equilibrium is completely analyzed, as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops. The bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold. In particular, the nature of Hopf and more degenerate, higher codimension bifurcations are explicitly determined.

引用

页码：1402 / 1424

页数：23

共 18 条

[1]

BEUTER A, 1989, J MOTOR BEHAV, V21, P277

[2] FEEDBACK AND DELAYS IN NEUROLOGICAL DISEASES - A MODELING STUDY USING DYNAMIC-SYSTEMS [J].