Abstract
This paper investigates the bifurcation phenomenon of fractional-order discrete-time chaotic systems and proposes the nonlinear control to synchronize two fractional-order discrete-time chaotic systems. By taking a finite truncation, fractional-order discrete-time chaotic systems are constructed. Chaotic phenomenon is also determined by the fractional-order. By adjusting the fractional order appropriately, the chaotic areas can be controlled. The synchronization control is designed for the same and different fractional-orders in the drive and response systems. Finally, the bifurcation phenomenon and synchronization of fractional-order Logistic system are studied. The proposed method can be extended to synchronize other fractional-order discrete-time systems.
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