Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation

Abstract

A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ⩾ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ⩾ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.1448, L2 = 0.0328, L3 = 0 and L4 = −1.1294. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY= 3.1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.

Keywords

• hyperchaos
• hyperjerk system
• adaptive control
• backstepping control
• synchronization