Chapter 5 - A new 3-D chaotic jerk system with a saddle-focus rest point at the origin, its active backstepping control, and circuit realization

Abstract

Jerk systems are important classes of 3-D mechanical systems. The analysis and their control of jerk dynamical systems have good applications in engineering. This chapter proposes a new 3-D chaotic jerk system with two quadratic nonlinear terms. We show that the jerk system has a unique rest point at the origin, which is an unstable saddle-focus rest point. We also show that the new jerk system shows multi-stability with coexisting attractors. In this chapter, we aim to control the chaotic behavior of the new mechanical jerk chaotic system. We discuss the qualitative behavior of the new jerk system in detailing with bifurcation diagrams. Backstepping control is applied to controlling and synchronizing the chaos in the proposed jerk chaotic system. A circuit for the new chaotic jerk dynamical system has been designed using Multisim to enable the practical implementation of the proposed jerk system.