A class of unexcited hyperjerk systems with megastability and its analog and microcontroller-based embedded system design

Abstract

Discovering chaotic systems with special features is of interest in the recent years. In this paper we introduce a new class of simple hyperjerk systems with infinitely coexisting chaotic attractors usually termed as megastability. The novelty of the proposed systems is that the systems shows megastability without external excitation which was not the case in most of the existing megastable attractors discussed in the literatures. Various dynamical properties of one of the proposed systems like the stability of equilibrium points, bifurcation and Lyapunov spectrum are discussed. Also, a circuit realization using off-the-shelf components is shown to prove the implementation feasibility of the systems. In addition, microcontroller based embedded design with graphic LCD of obtained new simple hyperjerk megastable oscillators was realized. Thus, the obtained new oscillators can be used both in a variety of real digital applications such as random number generators, encryption, communication and for educational purposes.