Synchronization in fractional-order differential systems

An ω-symmetrically coupled system consisting of identical fractional-order differential systems including chaotic and non-chaotic systems is investigated in this paper. Such a coupled system has, in its synchronous state, a mode decomposition by which the linearized equation can be decomposed into motions transverse to and parallel to the synchronous manifold. Furthermore, the decomposition can induce a sufficient condition on synchronization of the overall system, which guarantees, if satisfied, that a group synchronization is achieved. Two typical numerical examples, fractional Brusselators and the fractional Rössler system, are used to verify the theoretical prediction. The theoretical analysis and numerical results show that the lower the order of the fractional system, the longer the time for achieving synchronization at a fixed coupling strength.