A realizable chaotic system with interesting sets of equilibria, characteristics, and its underactuated predefined-time sliding mode control

Abstract

This paper presents a new 4D chaotic system having both single-scroll and double-scroll, self-excited and hidden attractors with the variation of system parameters. The proposed system exhibits several equilibrium points and their associated attractors. There are four interseting sets of equilibria with self-excited and hidden attractors. The system characteristics are demonstrated using phase plots, bifurcation diagrams and Lyapunov exponents. Offset boosting, amplitude control, the coexistence of attractors and antimonotonicity are demonstrated by the new system. Further, a predefined-time sliding mode controller with three control inputs for a 4D system is designed for successful synchronization between the two identical master and slave systems. Such an underactuated controller for synchronization is seldom seen in the literature. The developed 4D chaotic system is realized first using the NI Multisim circuit simulator and then in an NI Academic RIO hardware platform. The outcomes validate the numerical results.