Bogdanov–Takens singularity in the simple memristive time-delay system

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.