Hybrid synchronization phenomenon in two coupled delay hyperchaotic Lorenz systems with unknown parameters via a single linear controller

This work is devoted to investigating the hybrid synchronization phenomenon of two identical hyperchaotic Lorenz time-delay systems with different initial conditions, and a simple coexistence of anti-phase and complete synchronization scheme only with a single variable controller is proposed. Based on the Lyapunov stability theory, sufficient conditions of synchronization are obtained for both linear feedback and adaptive control approaches. The problem of adaptive synchronization between two nearly identical chaotic systems with unknown parameters is also studied. A single input adaptive synchronization controller is proposed and the adaptive parameter update laws are developed. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.