In this paper, we investigate a class of discontinuous Cohen-Grossberg neural networks (DCGNNs) with time-varying delays. Under the framework of Filippov solution, by means of differential inclusions theory and the set-valued version of the Mawhin coincidence theorem, we firstly establish the existence results of $2kT$-periodic solutions for the proposed DCGNNs. Secondly, by applying an approximation technique, we prove that the limit of the $2kT$-periodic solutions exists and the limit is exactly the homoclinic solution of the proposed DCGNNs. Thirdly, by using the non-smooth analysis theory with Lyapunov-like approach, some new testable algebraic criteria are derived for ensuring the global exponential stability of the solutions. It should be regarded as the first time to study the homoclinic solutions of Cohen-Grossberg neural networks with discontinuous activations based on Filippov solution. Finally, convincing numerical examples and remarks are provided to substantiate the superiority and efficiency of obtained results.

在本文中，我们研究了一类具有时变时滞的不连续Cohen-Grossberg神经网络（DCGNN）。在Filippov解的框架下，借助微分包含理论和Mawhin重合定理的集值版本，首先建立了$2ķŤ$提出的DCGNN的周期性解决方案。其次，通过应用逼近技术，我们证明了$2ķŤ$存在周期解，其极限恰好是所提出的DCGNN的同宿解。第三，通过将非光滑分析理论与类Lyapunov方法结合使用，得出了一些新的可检验代数准则，以确保解的全局指数稳定性。研究基于Filippov解的具有不连续激活的Cohen-Grossberg神经网络的同宿解应该被认为是第一次。最后，提供令人信服的数值示例和说明以证实所获得结果的优越性和效率。