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

• Published in: The European physical journal. ST, Special topics Vol. 231; no. 11-12; pp. 2445 - 2454
• Main Authors: Karami, Mahdi, Ramamoorthy, Ramesh, Ali, Ahmed M. Ali, Pham, Viet-Thanh
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2022; Springer Nature B.V
• Subjects: Atomic; Attraction; Bifurcation Delay and Multi Stability in Complex Nonlinear Systems; Bursting Oscillations; Classical and Continuum Physics; Condensed Matter Physics; Damping; Materials Science; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Oscillators; Physics; Physics and Astronomy; Regular Article; Unstable equilibrium point; Wave functions
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjs/s11734-021-00373-w

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.