A new oscillator with mega-stability and its Hamilton energy: Infinite coexisting hidden and self-excited attractors

Abstract

In this paper, we introduce an interesting new megastable oscillator with infinite coexisting hidden and self-excited attractors (generated by stable fixed points and unstable ones), which are fixed points and limit cycles stable states. Additionally, by adding a temporally periodic forcing term, we design a new two-dimensional non-autonomous chaotic system with an infinite number of coexisting strange attractors, limit cycles, and torus. The computation of the Hamiltonian energy shows that it depends on all variables of the megastable system and, therefore, enough energy is critical to keep continuous oscillating behaviors. PSpice based simulations are conducted and henceforth validate the mathematical model.