Multi-scroll hidden attractors with two stable equilibrium points.

Abstract

Multiscroll hidden attractors have attracted extensive research interest in recent years. However, the previously reported multiscroll hidden attractors belong to only one category of hidden attractors, namely, the hidden attractors without equilibrium points. Up to now, multiscroll hidden attractors with stable equilibrium points have not been reported. This paper proposes a multiscroll chaotic system with two equilibrium points. The number of scrolls can be increased by adding breakpoints of a nonlinear function. Moreover, the two equilibrium points are stable node-foci equilibrium points. According to the classification of hidden attractors, the multiscroll attractors generated by a novel system are the hidden attractors with stable equilibrium points. The dynamical characteristics of the novel system are studied using the spectrum of Lyapunov exponents, a bifurcation diagram, and a Poincaré map. Furthermore, the novel system is implemented by electronic circuits. The hardware experiment results are consistent with the numerical simulations.