Synchronization in Dynamically Coupled Fractional-Order Chaotic Systems: Studying the Effects of Fractional Derivatives

Abstract

This study presents the effectiveness of dynamic coupling as a synchronization strategy for fractional chaotic systems. Using an auxiliary system as a link between the oscillators, we investigate the onset of synchronization in the coupled systems and we analytically determine the regions where both systems achieve complete synchronization. In the analysis, the integration order is considered as a key parameter affecting the onset of full synchronization, considering the stability conditions for fractional systems. The local stability of the synchronous solution is studied using the linearized error dynamics. Moreover, some statistical metrics such as the average synchronization error and Pearson’s correlation are used to numerically identify the synchronous behavior. Two particular examples are considered, namely, the fractional-order Rössler and Chua systems. By using bifurcation diagrams, it is also shown that the integration order has a strong influence not only on the onset of full synchronization but also on the individual dynamic behavior of the uncoupled systems.