Prof. Xinsong Yang

Sichuan University

Speech title：Synchronization of Coupled Time-Delay Neural Networks with Mode-Dependent Average Dwell Time Switching

Abstract:

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. In this talk, a new concept is proposed to unify these switchings and global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations is investigated. A general switching mechanism with transition probability (TP) and mode-dependent average dwell time (MDADT) TP-based MDADT switching in this paper) is  introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and non-synchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided  to demonstrate the effectiveness and the merits of the theoretical analysis.