Synchronization of Neural Networks Involving Distributed-Delay Coupling: A Distributed-Delay Differential Inequalities Approach

In this article, we address the synchronization issue for coupled neural networks (CNNs) with mixed couplings by way of the delayed impulsive control, where the delay is distributed. Particularly, mixed couplings comprise the current-state coupling and the distributed-delay coupling, where influences on network connections caused by the past information of CNNs over a certain period are considered. First, we propose a novel array of delayed impulsive differential inequalities involving distributed-delay-dependent impulses, where distributed delays can be relatively larger. Second, we apply such delayed inequalities to analyze the problem of synchronization for CNNs with two different topologies. Sufficient criteria and distributed-delay-dependent impulsive controller are derived thereby. Furthermore, using techniques of matrix decomposition, several low-dimensional criteria are set out, which are appropriate for applications of large scale CNNs. Finally, a numerical example of CNNs with both the current-state coupling and the distributed-delay coupling involving three cases, are exhibited to exemplify the validity and the efficiency of the obtained theoretical results.

Automated summary

This article addresses the synchronization issue for coupled neural networks with mixed couplings using delayed impulsive control. Novel delayed impulsive differential inequalities involving distributed-delay-dependent impulses are proposed, and sufficient criteria and distributed-delay-dependent impulsive controller are derived for CNNs with different topologies. With the use of matrix decomposition techniques, low-dimensional criteria suitable for large scale CNN applications are set out, and the theoretical results are validated through numerical examples involving various cases.