Stability (learning theory)

Physics

Attractor

Mathematics

Torus

Algorithm

Statistical physics

Mathematical optimization

Machine learning

Hamiltonian system

Limit (mathematics)

Hamiltonian (control theory)

Mathematical analysis

Excited state

Artificial intelligence

Control (management)

Chaotic

Geometry

Computer science

Computation

Fixed point

Quantum mechanics

Control theory (sociology)

Limit cycle

Chaos An Interdisciplinary Journal of Nonlinear Science

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.

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