Analytical and Numerical Study of the Projective Synchronization of the Chaotic Complex Nonlinear Systems with Uncertain Parameters and Its Applications in Secure Communication

Abstract

The main aim of this research is to find an analytical and numerical study to investigate the projective synchronization of two identical or nonidentical chaotic complex nonlinear systems with uncertain parameters. The secure communication between these systems is achieved based on this study. Based on the adaptive control technique and the Lyapunov function a scheme is designed to achieve projective synchronization of chaotic attractors of these systems. The projective synchronization of two identical complex Chen systems and two different chaotic complex Lü and Lorenz systems is taken as two examples to verify the feasibility of the presented scheme. These chaotic complex systems appear in several applications in physics, engineering, and other applied sciences. Numerical simulations are calculated to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results. The above results will provide theoretical foundation for the secure communication applications based on the proposed scheme.