Novel Nonlinear Function Shift Method for Generating Multiscroll Attractors Using Memristor-Based Control Circuit

In this paper, a novel nonlinear function shift method for generating multiscroll attractors is proposed, and a memristor-based control circuit is used to realize the shift controller. Three types of shift modes, namely, horizontal shift, vertical shift, and combined shift, are added in a Jerk system. The dynamic behavior is analyzed through equilibria distribution, bifurcation diagram, Lyapunov exponent spectrum, and phase portraits. Research shows that various equilibria distributions and bifurcation phenomena can be obtained by adding different shifts, thereby producing diverse attractors including periodic orbits, single-scroll, double-scroll, and multiscroll attractors. Furthermore, symmetrical and asymmetrical attractors that are unusual dynamic behaviors can also be found. The circuit construction based on CMOS technology is given, and a memristor-based control circuit is designed to implement the proposed shift method. Different multiscroll attractors can be obtained by regulating the applied control signals instead of redesigning the nonlinear circuit, which simplifies the circuit design of multiscroll system. Our theoretical analysis, numerical simulations, and PSpice simulations together demonstrate the simpleness and effectiveness of the proposed methodology.