Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
Articles
Yuting Cai
Northeast Forestry University, China
Chunrui Zhang
Northeast Forestry University, China
Published 2017-09-24
https://doi.org/10.15388/NA.2017.5.2
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Keywords

delay
Hopf-pitchfork bifurcation
stability
coupled van der Pol model
normal form

How to Cite

Cai, Y. and Zhang, C. (2017) “Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay”, Nonlinear Analysis: Modelling and Control, 22(5), pp. 598–613. doi:10.15388/NA.2017.5.2.

Abstract

In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, bifurcation diagrams and phase portraits are given through analyzing the unfolding structure. Finally, numerical simulations are used to support theoretical analysis.

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