Generating grid chaotic sea from system without equilibrium point

Abstract

The dynamical system without equilibrium point is considered having hidden dynamics. It is relatively difficult to locate the attractor in the state space as its attraction basin has nothing to do with the equilibrium point. Especially, generation of multi-scroll chaos from no-equilibrium system is a challenging task. In this paper, using sine function, a modified Sprott-A system without equilibrium point but with perpetual points is presented. In particular, this system has the conservative property of zero-sum Lyapunov exponents and thus can generate chaotic sea rather than an attractor. The locations of the scrolls of chaotic sea are found having potential relevance to the sine nonlinearities and perpetual points. Different number of scrolls can be extended only adjusting the system parameters. Three cases of five-term Sprott-A system variants with single-direction multi-scroll/multi-double-scroll chaotic sea and two-direction grid chaotic sea are demonstrated. Besides, hidden tori are found coexisting with the chaotic sea. Numerical simulations and hardware experiments both confirm the complex dynamics of the system.