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arXiv · 1705.03794

Global Hopf bifurcation for differential-algebraic equations with state dependent delay

Qingwen Hu
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Abstract

We develop a global Hopf bifurcation theory for differential equations with a state-dependent delay governed by an algebraic equation, using the $S^1$-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.

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Qingwen Hu. 2017-08-29. Global Hopf bifurcation for differential-algebraic equations with state dependent delay. https://doi.org/10.1007/s10884-017-9640-0

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