A Novel Megastable System: Cloud, Kite, and Arrow-Like Attractors and Their Dynamics

Abstract

A megastable oscillator with various types of attractors is proposed. The oscillator shows interesting dynamics like cloud, kite, and arrow-like attractors. As we know, such a megastable oscillator with the dynamic shapes was not previously reported. There is an infinite number of arrow-like attractors in this oscillator. Investigating equilibrium points of the oscillator and their stabilities shows that two of the attractors, the largest cloud-like and smallest kite-like, are self-excited, while the others are hidden. The basin of attraction for the oscillator is studied for various attractors. Then, a forcing term is added to the oscillator, and its dynamics are investigated. The bifurcations and Lyapunov exponents of each type of attractor are investigated by changing the coefficient of the sinusoidal term [Formula: see text]. Each of the attractors shows various periodic, quasi-periodic, and chaotic dynamics for various [Formula: see text]. Also, the basin of attraction of the forced oscillator is investigated.