finite-time synchronization

This paper constructs a new complex hyper-chaotic system with attractive coexisting dynamic behaviors. We analyze the hyper-chaotic attractors, equilibrium points, Poincaré maps, Kaplan-York dimension, and Lyapunov exponent behaviors. The characteristics of hyper-chaotic systems include higher complexity, higher parametric resistance and sensitivity to very small changes in initial conditions. We prove that the introduced hyper–chaotic system is much more complex than the similar hyper-chaotic systems, that can suitable for use in encryption and secure communication. Next, the work describes a fast terminal sliding mode controller scheme for the fast synchronization and stability of the new complex hyper–chaotic system. It is shown that by applying uncertainty to the system, both steps of the sliding mode control have finite-time convergence properties. Next, a comparison will be made between a newly designed controller and a similar. Finally, using the MATLAB simulation, the results are confirmed for the new system. The results shown that the new hyper-chaotic system with many adsorbents is much more complex than similar systems, and the proposed controller has a faster convergence response than the similar controller.