Global synchronization of biological network systems with time-varying delays

This paper focuses on global synchronization of a class of biological network systems with time-varying delays. In particular, an excitatory and inhibitory biological neuronal network system with time-varying delays is proposed and its global synchronization is then further investigated. Some sufficient conditions for global synchronization of this system are attained based on Barbalat's lemma and linear matrix inequalities (LMIs). Moreover, an intriguing scenario of such a system asymptotically converging to a constant time-delay system (called a limiting delay system) is also discussed, and the result is obtained by saying that the original system is globally asymptotically synchronized if the new constant time-delay system is globally asymptotically synchronized under some conditions. Two numerical examples are given to illustrate the effectiveness of the proposed results.