A novel memristor-based dynamical system with multi-wing attractors and symmetric periodic bursting

This paper presents a novel memristor-based dynamical system with circuit implementation, which has a 2 × 3-wing, 2 × 2-wing, and 2 × 1-wing non-Shilnikov type of chaotic attractors. The system has two index-2 saddle-focus equilibria, symmetrical with respect to the x-axis. The system is analyzed with bifurcation diagrams and Lyapunov exponents, demonstrating its complex dynamical behaviors: the system reaches the chaotic state from the periodic state through alternating period-doubling bifurcations and then from the chaotic state back to the periodic state through inverse bifurcations, as one parameter changes. It shows two interesting phenomena: a jump-switching periodic state and jump-switching chaotic state. Also, the system can sustain chaos with a constant Lyapunov spectrum in some initial conditions and a parameter set. In addition, a class of symmetric periodic bursting phenomena is surprisingly observed under a particular set of parameters, and its generation mechanism is revealed through bifurcation analysis. Finally, the circuit implementation verifies the theoretical analysis and the jump-switching numerical simulation results.