Resonant hopf-hopf interactions in delay differential equations

被引：32

作者：

Campbell S.A. ^{[1
,2
]}

LeBlanc V.G. ^{[3
]}

机构：

[1] Department of Applied Mathematics, University of Waterloo, Waterloo

[2] Center for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montréal, Qué.

[3] Department of Mathematics and Statistics, University of Ottawa, Ottawa

来源：

Journal of Dynamics and Differential Equations | 1998年 / 10卷 / 2期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Delay differential equations; Normal forms; Resonant double hopf bifurcation;

D O I：

10.1023/A:1022622101608

中图分类号：

学科分类号：

摘要：

A second-order delay differential equation (DDE) which models certain mechanical and neuromechanical regulatory systems is analyzed. We show that there are points in parameter space for which 1:2 resonant Hopf-Hopf interaction occurs at a steady state of the system. Using a singularity theoretic classification scheme [as presented by LeBlanc (1995) and LeBlanc and Langford (1996)], we then give the bifurcation diagrams for periodic solutions in two cases: variation of the delay and variation of the feedback gain near the resonance point. In both cases, period-doubling bifurcations of periodic solutions occur, and it is argued that two tori can bifurcate from these periodic solutions near the period doubling point. These results are then compared to numerical simulations of the DDE. © 1998 Plenum Publishing Corporation.

引用

页码：327 / 346

页数：19

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