A simple chaotic circuit with magnetic flux-controlled memristor

In this paper, we build a simple chaotic circuit by introducing a new magnetic flux-controlled memristor model. The basic dynamics, such as the type of equilibrium point, phase diagram, bifurcation diagram, and Lyapunov exponent spectrum, are studied theoretically and numerically. It is found that this memristor circuit has complex nonlinear behavior, including coexistence bifurcation, transient dynamics, and anti-monotonicity. The salient feature of the memristor chaotic circuit is that the initial conditions of both the memristor and system can realize the modulation of the position and amplitude of the attractor. To verify the chaotic characteristics of the system, an analog circuit is designed and the experimental results provide the consistency with the numerical simulation.