Stabilization and Synchronization of a New 3D Complex Chaotic System via Adaptive and Active Control Methods

This paper investigates the controllability and synchronization of a newly designed three-dimensional chaotic system using active and adaptive control strategies. Although both controllers were designed with the help of a positive definite function using Lyapunov theory, for adaptive controllers, we estimated an unknown parameter of the system in real time and adjusted the control signal accordingly to maintain stability. Moreover, numerical simulations demonstrated that the active control approach achieved stability for both equilibrium points (p1 and p2) approximately at time t = 0.5 s, demonstrating its rapid convergence and robust performance. In contrast, the adaptive control method stabilized p1 at approximately t≈0.5 and p2 at t≈1 s, illustrating reaching their desired conditions. Furthermore, the considered methods could effectively synchronize two identical chaotic systems, where the slave system overlapped the master system at approximately t=5 s. Apart from this, a detailed comparative analysis of the two techniques in terms of controllability and synchronization is presented. Moreover, the complementary strengths of these methods provide valuable perspectives for broader applications in chaotic system management and security-critical systems.