A New Multi-Scroll Megastable Oscillator Based on the Sign Function

Abstract

A chaotic system that can show multiscroll and megastable attractors is studied in this paper. Two cases of the system with periodic and quasi-periodic excitations are discussed. Various stabilities of the system determined by changing parameters and initial values are investigated for both cases. In Case-A of the proposed system, multiscroll attractors are shown for the various parameter values. In Case-B with quasi-periodic excitation, the system shows various multiscroll attractors. Dynamical properties of these two cases are studied using the bifurcation diagram and Lyapunov exponents.