Design and Stability Analysis of Adaptive Synchronization Control Strategies for Integer and Fractional Chaotic Systems

Chaotic synchronization plays an important role in nonlinear dynamics, secure communications, and complex information systems, yet parameter uncertainty remains a major obstacle to practical implementation. This study proposes a unified adaptive synchronization control strategy for both integer-order and fractional-order chaotic systems under unknown parameter conditions. Based on Lyapunov stability theory, generalized controller structures and adaptive parameter update laws are designed to achieve robust synchronization independent of specific system forms. Stability analysis theoretically proves asymptotic synchronization and bounded convergence of parameter estimation errors. Numerical simulations using representative Lorenz and fractional-order Chen systems verify the effectiveness and robustness of the proposed method. Results demonstrate rapid synchronization error convergence and accurate parameter estimation under uncertain conditions. The proposed framework provides theoretical support for nonlinear control systems and offers application potential in secure communications, electromagnetic signal transmission, and complex dynamic network synchronization.