Adaptive adjustment strategy designs for couplings against nonlinear networks

This paper is concerned with the robust synchronization problem of a class of nonlinearly complex networks via adaptive adjustor designs. An adaptive adjustment strategy is addressed to adjust coupling strength to compensate the effect of nonlinear perturbations. Then, based on the adaptive adjustments, an approach that is application of Lyapunov stability theory for the synchronization error system is introduced to prove the robust synchronization of the overall networks. It is shown that, the result can be established for any nonlinear coupling network even without control inputs. Finally, simulation results are given to verify the effectiveness of the proposed method.