Simple megastable oscillators with different types of attractors; tori, chaotic and hyperchaotic ones

Coexistence of attractors with different or same type, multistability, is a complex behavior in nonlinear systems. This feature makes these systems applicable but difficult to control. Besides multistability, some new systems show megastability, existence of infinite number of coexisting attractors. In this paper, two simple megastable systems are presented in details. Moreover, these systems show hyperchaotic behavior which is rare in these types of systems as previously proposed systems mostly show chaos and periodic responses. To show the properties of these systems, nonlinear analytical tools are used in this article.