Carpet oscillator: A new megastable nonlinear oscillator with infinite islands of self-excited and hidden attractors

Abstract

In this paper, we design a new two-dimensional nonlinear oscillator with infinite number of coexisting limit cycles distributed in a plane. One-third of these limit cycles are self-excited attractors while two-third of them are hidden attractors. Modifying this new system to its forced version, we obtain a new nonlinear system with infinite number of coexisting torus attractors and limit cycle attractors.