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

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.

A Giga-Stable Oscillator with Hidden and Self-Excited Attractors: A Megastable Oscillator Forced by His Twin.

In this paper, inspired by a newly proposed two-dimensional nonlinear oscillator with an infinite number of coexisting attractors, a modified nonlinear oscillator is proposed. The original system has an exciting feature of having layer-layer coexisting attractors. One of these attractors is self-excited while the rest are hidden.