Complex projective synchronization in drive-response networks coupled with complex-variable chaotic systems. (English) Zbl 1268.34099

Summary: In drive-response complex-variable systems, projective synchronization with respect to a real number, real matrix, or even real function means that drive-response systems evolve simultaneously along the same or inverse direction in a complex plane. However, in many practical situations, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, this paper investigates projective synchronization in drive-response networks of coupled complex-variable chaotic systems with respect to complex numbers, called complex projective synchronization (CPS). The adaptive feedback control method is adopted first to achieve CPS in a general drive-response network. For a special class of drive-response networks, the CPS is achieved via pinning control. Furthermore, a universal pinning control scheme is proposed via the adaptive coupling strength method, several simple and useful criteria for CPS are obtained, and all results are illustrated by numerical examples.


34D06 Synchronization of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
93C40 Adaptive control/observation systems
Full Text: DOI


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