Impulsive Effects Based Distributed Synchronization of Heterogeneous Coupled Neural Networks

This paper is devoted to investigating the exponential synchronization problem on a class of coupled heterogeneous neural networks with hybrid time-varying delays. Since the heterogeneity of neural networks, the quasi-synchronization rather than complete synchronization is studied. Consider that the controller would suffer from impulsive disturbances, the distributed pinning control strategy is introduced. By jointly applying the concept of average impulsive intervals, the extended comparison principle of impulsive systems, and the vector norm techniques, sufficient conditions for the achievement of exponential quasi-synchronization on coupled heterogeneous neural networks are eventually obtained. In view that different impulsive effects play different roles in network synchronizing, two different situations of exponential synchronization are considered, respectively, by separately discussing the impulsive-effects-related parameter. Additionally, on account of the extended parameter variation formula for impulsive systems with hybrid time-varying delays, the exponential convergence velocities and the quasi-synchronization errors are estimated, separately, with respect to different ranges of impulsive effects. At last, three numerical examples with distinct impulsive effect values are given to illustrate the effectiveness of the theoretical analysis and the control schemes.

Automated summary

This paper investigates the exponential synchronization problem on a class of coupled heterogeneous neural networks with hybrid time-varying delays by introducing a distributed pinning control strategy. Sufficient conditions for achieving exponential quasi-synchronization are obtained by applying the concept of average impulsive intervals, the extended comparison principle of impulsive systems, and vector norm techniques. Two different situations of exponential synchronization are considered based on the different roles of impulsive effects in network synchronizing.