Synchronization of fractional-order colored dynamical networks via open-plus-closed-loop control

In this paper, the synchronization of a fractional-order colored complex dynamical network model is studied for the first time. In this network model, color edges imply that both the outer coupling topology and the inner interactions between any pair of nodes may be different, and color nodes mean that local dynamics may be different. Based on the stability theory of fractional-order systems, the scheme of synchronization for fractional-order colored complex dynamical networks is presented. To achieve the synchronization of a complex fractional-order edge-colored network, the open-plus-closed-loop (OPCL) strategy is adopted and effective controllers for synchronization are designed. The open-plus-closed-loop (OPCL) strategy avoids the need for computation of eigenvalues of a very large matrix. Then, a synchronization method for a class of fractional-order colored complex network, containing both colored edges and colored nodes, is developed and some effective synchronization conditions via close-loop control are presented. Two examples of numerical simulations are presented to show the effectiveness of the proposed control strategies.