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

  • Qingwen Hu
Article
  • 479 Downloads

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.

Keywords

State-dependent delay Hopf bifurcation Differential-algebraic equations \(S^1\)-equivariant degree Regulatory dynamics 

Notes

Acknowledgements

The author would like to thank an anonymous referee for the detailed and constructive comments.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesThe University of Texas at DallasRichardsonUSA

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