Eur. Phys. J. Spec. Top. (2022) 231: 2445-2454
https://doi.org/10.1140/epjs/s11734-021-00373-w

Regular Article

Jagged-shape chaotic attractors of a megastable oscillator with spatially square-wave damping

¹ Reticom Solutions Inc., 2950 Kew Dr, N8T 3G7, Windsor, ON, Canada
² Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, India
³ Department of Power Mechanics, Babylon Technical Institute, Al-Furat Al-Awsat Technical University, 51001, Babylon, Iraq
⁴ Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^d phamvietthanh@tdtu.edu.vn

Received: 18 August 2021
Accepted: 7 December 2021
Published online: 17 December 2021

Abstract

Here, a 2D megastable oscillator with a square-wave function is proposed. The oscillator shows an infinite number of coexisting jagged-shape limit cycles. It has an unstable equilibrium point. Based on this equilibrium, the innermost attractor is self-excited, while the other ones are hidden. The number of sharp edges of the jagged-shape limit cycles increases by moving the attractor from the innermost one toward the outside. The basin of attraction of the limit cycles is also studied. Then, a sinusoidal force is applied to the oscillator, and its chaotic dynamics are discussed. Various dynamics of the forced oscillator by changing the amplitude and frequency of the forced term are discussed. The basin of attraction of the forced system is investigated. To the best of our knowledge, the jagged-shape attractors in multi-stable oscillators have not been studied before.