A new kind of nonlinear phenomenon in coupled fractional-order chaotic systems: coexistence of anti-phase and complete synchronization

In this paper, we have found a kind of interesting nonlinear phenomenon—-hybrid synchronization in linearly coupled fractional-order chaotic systems. This new synchronization mechanism, i.e., part of state variables are anti-phase synchronized and part completely synchronized, can be achieved using a single linear controller with only one drive variable. Based on the stability theory of the fractional-order system, we investigated the possible existence of this new synchronization mechanism. Moreover, a helpful theorem, serving as a determinant for the gain of the controller, is also presented. Solutions of coupled systems are obtained numerically by an improved Adams—Bashforth—Moulton algorithm. To support our theoretical analysis, simulation results are given.