Projective lag synchronization in drive-response dynamical networks with delay coupling via hybrid feedback control

Abstract

This paper investigates the problem of projective lag synchronization behavior with delayed coupling in drive-response dynamical network model consisting of identical and nonidentical nodes. Based on Lyapunov stability theory, a hybrid feedback control method is designed to achieve the projective lag synchronization with constant time delay and with time-varying coupling delay. In addition, the control will deal with and without mismatched terms. Finally, analytical results show that the states of the dynamical network with delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulation results demonstrate the validity of the proposed method.