Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances

Abstract

This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.