A new 4-D hyperchaotic hyperjerk system with a single equilibrium, its dynamic properties and circuit design

Abstract

This paper announces a new four-dimensional hyperchaotic hyperjerk system with a single equilibrium and discusses its dynamic properties such as Lyapunov exponents, phase portraits, Kaplan-Yorke dimension and equilibrium points. Hyperjerk systems have a nice triangular structure in their dynamics and they have many engineering applications. Our new hyperjerk system has three nonlinearities in total. New synchronization results based on active backstepping control are also derived for the new hyperjerk system. In addition, an electronic circuit implementation of the new hyperjerk system is designed carefully and examined well in MultiSIM. A good qualitative agreement has been shown between the MATLAB simulations of the theoretical hyperchaotic hyperjerk model and the MultiSIM results.