Dynamics investigation and chaos-based application of a novel no-equilibrium system with coexisting hidden attractors

Abstract

This work presents a novel three-dimensional system with multiple types of coexisting attractors (including chaotic, periodic, quasi-periodic, and unbound divergent orbit) that are categorized as hidden attractors and investigates its dynamics via the Lyapunov exponent spectrum, phase diagrams, and basins of attraction. The mechanism of the emergence of chaos is explored through numerical simulation. Under some conditions, the periodic orbits embedded in the new system without equilibria are studied using the variational method, and effective symbolic coding with four letters is successfully established to classify all short cycles. The symbols proposed by the method are highly consistent with the calculated results. Furthermore, the analogous circuit implementation is executed to demonstrate the flexibility and validity of the new system that possesses coexisting attractors. Finally, chaos-based applications of the new system, including synchronization, offset boosting control, and image encryption, are presented to show system’s feasibility.