Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters

This paper introduces a new type of synchronization method of adaptive modified projective synchronization with complex scaling matrix (ACMPS) for two $$n$$n-dimensional complex chaotic (hyperchaotic) systems with uncertain complex parameters. By choosing appropriate Lyapunov functions dependent on complex variables, and employing adaptive control technique, sufficient criteria on ACMPS are derived. Moreover, in the complex space, the slave system can be asymptotically synchronized up to nonidentical or identical master system by a desired complex scaling matrix, and all of unknown parameters in both master and slave systems are achieved to be identified by virtue of the complex update laws. Finally, two examples are worked out to verify the effectiveness and feasibility of the theoretical results.

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