A New Hyperchaotic Hyperjerk System with Three Nonlinear Terms, its Synchronization and Circuit Simulation

Abstract

In recent decades, hyperjerk systems have been studied well in the literature because of their simple dynamics structure and complex qualitative properties. In this work, we announce a new hyperchaotic hyperjerk system with three nonlinear terms. Dynamical properties of the hyperjerk system are analyzed through equilibrium analysis, dissipativity, phase portraits and Lyapunov chaos exponents. We show that the new hyperchaotic hyperjerk system has a unique saddle-focus equilibrium at the origin. Thus, the new hyperchaotic hyperjerk system has a self-excited strange attractor. Next, global hyperchaos synchronization of a pair of new hyperchaotic hyperjerk systems is successfully achieved via adaptive backstepping control. Also, an electronic circuit of the hyperchaotic hyperjerk system has been designed via MultiSIM to check the feasibility of the theoretical system.