Abstract Competitive neural networks have become increasingly popular since this kind of neural networks can better describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications. In this paper, we first propose fractional-order competitive neural networks with multiple time-varying-delay links and explore the global asymptotic stability of this class of neural networks. A novel and generalized integral inequality related to every upper bound of each time-varying delay is given. Moreover, based on Lyapunov method and graph theory, we obtain some sufficient conditions with the help of this integral inequality to guarantee the global asymptotic stability. The theoretical results offer a new perspective to show the close relationship between the stability criterion and the topological structure of networks. Finally, an illustrative numerical example is given to demonstrate the feasibility and effectiveness of the theoretical results.

中文翻译：

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具有多个时变延迟链接的分数阶竞争神经网络的全局渐近稳定性

摘要 竞争性神经网络变得越来越流行，因为这种神经网络可以更好地描述具有无监督突触修饰的皮层认知图的动态。在本文中，我们首先提出了具有多个时变延迟链接的分数阶竞争神经网络，并探索了此类神经网络的全局渐近稳定性。给出了与每个时变延迟的每个上限相关的新颖的广义积分不等式。此外，基于Lyapunov方法和图论，我们借助这个积分不等式得到了一些充分条件来保证全局渐近稳定性。理论结果为显示稳定性判据与网络拓扑结构之间的密切关系提供了新的视角。最后，