In this paper, the concept of Lipschitz stability is introduced to impulsive delayed reaction-diffusion neural network models of fractional order. Such networks are an appropriate modeling tool for studying various problems in engineering, biology, neuroscience and medicine. Fractional derivatives of Caputo type are considered in the model. The effects of impulsive perturbations and delays are also under consideration. Lipschitz stability analysis is performed and sufficient conditions for global uniform Lipschitz stability of the model are established. The Lyapunov function approach combined with the comparison principle are employed in the development of the main results. The proposed criteria extend some existing stability results for such models to the Lipschitz stability case. The introduced concept is also very useful in numerous inverse problems.

本文将Lipschitz稳定性的概念引入分数阶脉冲延迟反应-扩散神经网络模型中。这种网络是研究工程、生物学、神经科学中各种问题的合适建模工具和药。模型中考虑了 Caputo 类型的分数导数。脉冲扰动和延迟的影响也在考虑之中。进行了Lipschitz稳定性分析，建立了模型全局均匀Lipschitz稳定性的充分条件。Lyapunov 函数方法与比较原理相结合用于主要结果的开发。建议的标准将此类模型的一些现有稳定性结果扩展到 Lipschitz 稳定性案例。引入的概念在许多逆问题中也非常有用。