Discrete-time Complex Dynamical Networks Research Articles

Synchronization criterions and pinning control of general complex networks with time delay

The problems of synchronization and pinning control for general time-delay complex dynamical networks are investigated. In this paper, less conservative criterions for both continuous-time and discrete-time complex dynamical networks with time delay are obtained. Pinning control strategies are respectively, designed to make these complex dynamical networks synchronized. Moreover, the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities, which reduces the computation complexity. Finally, numerical simulations verify the effectiveness of our methodology.

Impulsive synchronization of general continuous and discrete-time complex dynamical networks

This paper mainly investigates the impulsive synchronization of a general complex continuous and discrete-time dynamical network. Firstly, for the continuous complex networks, we give a sufficient condition to guarantee its synchronization. When the sufficient condition is not satisfied, the impulsive controllers are utilized, and some novel criteria are derived to guarantee the network synchronization in this case. What is more significant is that the similar work is extended to the discrete-time networks model. Finally, the results are, respectively, illustrated by a continuous network composed with the chaotic Chen oscillators and a discrete-time network consisting of Hénon map. All numerical simulations verify the effectiveness of the theoretical analysis.

Stability analysis of synchronization in discrete-time complex dynamical networks

In this paper, by using both the linear stability analysis and Lyapunov function approach, some conditions for stabilizing synchronization behavior in a discrete-time complex dynamical network were derived. These conditions were determined by the coupling strength and the eigenvalues of coupling configuration matrix. Furthermore, some explicit results were obtained when the coupling map between the nodes is equal to the dynamics function of the network, which implies that the product of the coupling strength and the eigenvalues is bounded.