A symmetric oscillator with multi-stability and chaotic dynamics: bifurcations, circuit implementation, and impulsive control

Abstract

Finding chaotic oscillators with unique properties is a hot topic. In this paper, a symmetric oscillator with multi-stability is proposed. This oscillator has bounded dynamics for any initial conditions. It is also shown that the oscillator has one unstable equilibrium. This paper studies the dynamical properties of the oscillator, such as chaotic attractors, Lyapunov exponents (LEs), bifurcation diagrams, and the basin of attraction. Its feasibility is shown by circuit implementation. In addition, the stabilization of the system is investigated by impulsive control.