Global Hopf Bifurcation for Differential-Algebraic Equations with State-Dependent Delay

被引：3
|
作者：
Hu, Qingwen [1 ]
机构：
[1] Univ Texas Dallas, Dept Math Sci, 800 West Campbell Rd, Richardson, TX 75080 USA
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2019年 / 31卷 / 01期
关键词：
State-dependent delay; Hopf bifurcation; Differential-algebraic equations; S-1-equivariant degree; Regulatory dynamics;
D O I：
10.1007/s10884-017-9640-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop a global Hopf bifurcation theory for differential equations with a state-dependent delay governed by an algebraic equation, using the S1-equivariant degree. We apply the global Hopf bifurcation theory to a model of genetic regulatory dynamics with threshold type state-dependent delay vanishing at the stationary state, for a description of the global continuation of the periodic oscillations.
引用
收藏
页码：93 / 128
页数：36
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