Abstract: This thesis deals with introducing real and complex nonlinear dynamical systems and studying their basic properties and chaos synchronization of their attractors. More specifically, we shall focus on the study of dynamical behaviors of these systems including the existence of equilibrium point and studying their stability. Sensitive dependence on initial conditions for these systems is generate chaotic behavior as well as attractors. Using Lyapunov's direct method and active control method to study the synchronization of chaotic attractors of t