Eur. Phys. J. Spec. Top. (2022) 231: 2153-2161
https://doi.org/10.1140/epjs/s11734-021-00371-y

Regular Article

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

¹ School of Science, Xijing University, 710123, Xi’an, People’s Republic of China
² Centre for Additive Manufacturing, Chennai Institute of Technology, Chennai, India
³ Information Technology Collage, Imam Ja’afar Al-Sadiq University, 10001, Baghdad, Iraq
⁴ Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar

Received: 13 August 2021
Accepted: 7 December 2021
Published online: 26 December 2021

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.