A new chaotic hyperjerk system with a half-line of equilibrium points, its dynamic analysis, multistability, circuit simulation and anti-synchronization via backstepping control

In this work, we present a new four-dimensional chaotic hyperjerk system with a half-line of equilibrium points. In the chaos literature, it is well-known that chaotic systems with an infinite number of equilibrium points exhibit hidden attractors. Thus, we deduce in this research work that the new chaotic hyperjerk system has hidden attractors. We next study the new chaotic hyperjerk system for a dynamic analysis using bifurcation plots and Lyapunov Exponents (LE) diagrams.We exhibit that the new hyperjerk system has a special property of multistability with coexisting attractors. Using Multisim version 14.2, we carry out an electronic circuit simulation for the proposed 4-D chaotic hyperjerk system with a half-line of equilibrium points. Finally, as an application in control engineering, we apply backstepping control for achieving antisynchronization of a pair of new chaotic hyperjerk systems taken as master-slave systems, which has important applications in communication systems.