An ω-symmetrically coupled system consisting of identical fractional-order differential systems including chaotic and nonchaotic 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 Rossler 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.

We model a synthetic gene regulatory network in a microbial cell, and investigate the effect of noises on cell-cell communication in a well-mixed multicellular system. A biologically plausible model is developed for cellular communication in an indirectly coupled multicellular system.Without extracellular noises, all cells, in spite of interaction among them, behave irregularly due to independent intracellular noises. On the other hand, extracellular noises that are common to all cells can induce collective dynamics and stochastically synchronize the multicellular system by actively enhancing the integrated interchange of signaling molecules.