Journal
MATHEMATICS
Volume 11, Issue 23, Pages -Publisher
MDPI
DOI: 10.3390/math11234831
Keywords
coupled van der Pol oscillators; delay; symmetric Hopf bifurcation; periodic solution
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This paper studies a system of four coupled van der Pol oscillators with delay. The conditions for the existence of multiple periodic solutions of the system are given. The spatiotemporal patterns of the system are obtained using symmetric Hopf bifurcation theory. Numerical simulations are used to demonstrate the theoretical results.
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.
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