Bogdanov–Takens singularity in the simple memristive time-delay system
School of Mathematics and Physics, China University of Geosciences, 430074 Wuhan, P.R. China
2 Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, Guangxi 537000, P.R. China
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Received in final form: 1 March 2019
Published online: 14 October 2019
In this paper, a simple memristive system is considered. We obtain existence of Bogdanov–Takens (B–T) bifurcation at the equilibrium in the 2D memristive time-delay system. With the change of two bifurcation parameters, in particular, it will lead to different bifurcations when the delay passes a certain critical value. Based on center manifold and classic normal form method, Hopf, pitchfork, homoclinic, and double limit cycle bifurcation are derived.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019