Dynamic analysis, circuit realization, and its synchronization of a new chaotic hyperjerk system

Abstract This article presents a new chaotic hyperjerk system by adding nonlinear term to an existing model. The dissipativity and invariance, equilibrium points, and their stability conditions, as well as the conditions for the existence of Hopf bifurcations at the equilibrium points, are analyzed. Meanwhile, we investigate the rich dynamical phenomena of the hyperjerk system, and the results show that the system exhibits chaos over a wide range of parameter variations and demonstrates complex dynamical characteristics such as periodic orbits, multi-periodic orbits, and quasi-periodic orbits under different parameter conditions. Furthermore, the chaotic synchronization, and circuit implementation of the hyperjerk system are also studied. Finally, the application of the hyperjerk system in chaotic encryption and decryption is discussed.