Synchronization of coupled neural networks under mixed impulsive effects: A novel delay inequality approach

In this paper, the synchronization problems of an array of coupled neural networks with mixed impulses are considered. Here mixed impulses contain desynchronizing delay-free impulses, synchronizing delay-free impulses, desynchronizing delayed impulses and synchronizing delayed impulses. A novel concept named average delayed impulsive gain is proposed to quantify the effects of mixed impulses. Besides, we establish a delayed impulsive differential inequality which extends famous Halanay inequality, and apply it to study the synchronization problems of delayed neural networks with mixed impulses. It is interesting to notice that both delay-free impulses and delayed impulses can contribute to the synchronization of coupled neural networks. Meanwhile, we also discuss the synchronization of neural networks only with delay-dependent impulses. Some sufficient conditions are derived to ensure the exponential synchronization of delayed neural networks. Finally, some numerical examples are provided to illustrate the validity and superiority of the obtained results.