Chapter 9 - A new multistable plasma torch chaotic jerk system, its dynamical analysis, active backstepping control, and circuit design

Abstract

Jerk chaotic systems have many applications in science and engineering. In the past few decades, significant attention has been paid on the modeling of new jerk differential equations arising in engineering. An important model of a plasma torch jerk differential equation exhibiting chaos was reported by Ghorui et al. (2000). The Ghorui jerk system is a recent example of a jerk chaotic system consisting of a just cubic nonlinearity and linear terms in its dynamics. This work announces a new plasma torch jerk chaotic system by adding a quadratic nonlinearity to the Ghorui jerk chaotic system. We show that the new plasma torch jerk system has a self-excited chaotic attractor with three unstable saddle-foci rest points. We give a detailed bifurcation analysis of the new plasma torch chaotic jerk system. We also report that the new plasma torch chaotic jerk system has multistability and coexisting chaotic attractors. As control applications, we use active backstepping control laws for the global chaos stabilization and global chaos synchronization for the new plasma torch chaotic jerk system. Finally, we design an electronic circuit of the new plasma torch chaotic jerk system using Multisim for practical implementation in engineering.