Dynamical behavior and synchronization of hyperchaotic complex T-system

Abstract

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncertain parameters via adaptive control. For synchronization, we use less controllers than the dimension of the proposed system. Also, we prove that the error system is asymptotically stable by using a Lyapunov function. Numerical simulations are computed to check the analytical expressions.