A new megastable nonlinear oscillator with infinite attractors

Abstract

Dynamical systems with megastable properties are very rare in the literature. In this paper, we introduce a new two-dimensional megastable dynamical system with a line of equilibria, having an infinite number of stable states. By modifying this new system with temporally-periodic forcing term, a new two-dimensional non-autonomous nonlinear oscillator capable to generate an infinite number of coexisting limit cycle attractors, torus attractors and, strange attractors is constructed. The analog implementation of the new megastable oscillator is investigated to further support numerical analyses and henceforth validate the mathematical model.