A Megastable Oscillator with Two Types of Attractors

Abstract

In this paper, a megastable system is designed with particular formation of attractors. It has two formations of attractors: the inner ones with a smaller amplitude, and the outer ones with the Eye of God nebula shape and larger amplitude. To the best of our knowledge, such a megastable oscillator with this special formation of attractors has not been studied before. Afterward, the oscillator is forced, and its attractors are discussed. Different dynamics of this new oscillator are investigated using tools such as bifurcation and Lyapunov exponent diagram, and basins for each attractor. In this paper, a megastable system is designed with particular formation of attractors. It has two formations of attractors: the inner ones with a smaller amplitude, and the outer ones with the Eye of God nebula shape and larger amplitude. To the best of our knowledge, such a megastable oscillator with this special formation of attractors has not been studied before. Afterward, the oscillator is forced, and its attractors are discussed. Different dynamics of this new oscillator are investigated using tools such as bifurcation and Lyapunov exponent diagram, and basins for each attractor.