Abstract
Between two 4-dimensional hyper-chaotic systems with unknown parameters, using Lyapunov stability theory, adaptive controller and parameter estimation law are designed to achieve their globally asymptotical synchronization and anti-synchronization. By numerical calculation with MATLAB, synchronization or anti-synchronization is arrived theoretically but synchronous or anti-synchronous errors of state variables cannot all converge to zero simultaneously during a limited time. The comparative and contrastive studies about system without cubic term indicates that the primary cause is existence of cubic term. It is verified by numerical simulation examples consistently.
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