Extreme multi-stability and circuit implementation for a two-ReLU-memristor-based jerk oscillator

Abstract Memristor-based oscillation circuits are prone to produce coexisting infinite attractors depending on the initial conditions of memristors, leading to the appearance of extreme multi-stability. In this paper, we propose a novel memristive jerk oscillator by bringing two ReLU-type memristors in a simple jerk oscillator and investigate its dynamical behaviors associated with the coupling parameters using bifurcation plots and Lyapunov exponent plots. Further, we discuss the planar equilibrium state and its stability, and then numerically explore the coexisting infinite attractors driven by the initial conditions of two ReLU-type memristors. Because of the intervention of the two ReLU-type memristors, the memristive jerk oscillator has a planar equilibrium state whose stability closely relies on the initial conditions of two ReLU-type memristors, and different initial conditions cause different attractors to coexist, resulting in bidirectional extreme multi-stability. Finally, the memristive jerk oscillator is implemented by analog circuit and digital hardware platform, and the numerical results are confirmed by circuit simulations and hardware experiments.