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

Liqin Liu and Chunrui Zhang ()
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Liqin Liu: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Chunrui Zhang: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2023, vol. 11, issue 23, 1-16

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.

Keywords: coupled van der Pol oscillators; delay; symmetric Hopf bifurcation; periodic solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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