Dynamics, Periodic Orbits of a Novel Four-Dimensional Hyperchaotic System with Hidden Attractors

Abstract In recent years, the investigation of systems featuring hidden attractors and coexisting attractors has garnered significant attention. This paper presents a novel four-dimensional (4D) hyperchaotic system devoid of equilibrium points, achieved by formulating an equation without a solution or constructing a system without fixed points. Due to the complex shape of this attractor, a novel coding method is utilized to establish symbol dynamics using eight letters. The proposed system exhibits highly intricate dynamics, including variations in topological structure with alterations in system parameters, as well as an exploration and discussion of four types of coexisting attractors. Our extensive practice has led us to propose a new conjecture: hyperchaotic systems with parameters close to the bifurcation point frequently display multistable states. Furthermore, the unstable periodic orbits with different topological lengths in the hidden hyperchaotic attractor are calculated systematically using the variational method. Additionally, the DSP circuit implementation is employed to validate the numerical simulation results for this new 4D system. Finally, adaptive synchronization is successfully realized within the system, thereby confirming its feasibility.