Finite-time synchronization of a new five-dimensional hyper-chaotic system via terminal sliding mode control

This study constructs a new 5D nonlinear hyper-chaotic system with attractive and complex behaviors. The standard behaviors of the chaotic system will also be analyzed including: Equilibrium Point (EP), Bifurcation Diagram (BD), Poincare Map (PM), Lyapunov Exponent (LE), and Kaplan-Yorke dimensional. We prove that the introduced new 5D hyper-chaotic system has complex and nonlinear behaviors. Next, the work describes Fast Terminal Sliding Mode Control (FTSMC) scheme for the control and finite-time fast synchronization of the novel 5D nonlinear hyper-chaotic system. Proof of stability for both phases has been done for the new controller with the Lyapunov stability theory. To ensure synchronization, both master-slave subsystems are perturbed by different parameter and model uncertainties. Both steps of the Sliding Mode Controller (SMC) have chaos-based fast convergence properties. Subsequently, it has been shown that the state paths of both master-slave systems can reach each other in a limited time. One of the features of the novel controller in this paper is high performance and finite-time stability of the terminal sliding surface due to derivative error and other errors. Finally, by using the MATLAB simulation, the results are confirmed for the new hyper-chaotic system.