Applied Math PhD comprehensive exam | Kexue Zhang, Impulsive Control of Discrete-Time Complex Dynamical Networks with Time-Delay

Impulsive Control of Discrete-Time Complex Dynamical Networks with Time-Delay

Complex dynamical networks (CDNs) consist of a large set of interconnected nodes with each node being a fundamental unit with detailed contents. A great number of natural and man-made complex networks such as social networks, food networks, neural networks, the Work Wide Web, electrical power grid, etc., can be effectively modeled by CDNs. Since the wide existence of time-delay in the coupling channels among these individual nodes, the study of time-delay networks has received a great deal of attention over the past decades.

In this talk, I will (i) give an over view of CDNs and introduce the discrete-time model of CDNs with time-delay, (ii) introduce three kinds of control problems about CDNs: stabilization, synchronization and consensus, and discuss how to stabilize, synchronize and achieve consensus of time-delay discrete CDNs via the impulsive control method, (iii) introduce some new results about impulsive synchronization of discrete-time CDNs with coupling delays.