Multiple Hopf Bifurcations of Four Coupled van der Pol Oscillators with Delay

Author:

Liu Liqin1,Zhang Chunrui1ORCID

Affiliation:

1. Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Abstract

In this paper, a system of four coupled van der Pol oscillators with delay is studied. Firstly, the conditions for the existence of multiple periodic solutions of the system are given. Secondly, the multiple periodic solutions of spatiotemporal patterns of the system are obtained by using symmetric Hopf bifurcation theory. The normal form of the system on the central manifold and the bifurcation direction of the bifurcating periodic solutions are derived. Finally, numerical simulations are attached to demonstrate our theoretical results.

Funder

Fundamental Research Funds for the Central Universities

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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5. Positive invariant regions for a modified Van Der Pol equation modeling heart action;Acosta;Appl. Math. Comput.,2023

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