This paper is concerned with the periodic solutions for a class of stochastic Cohen–Grossberg neural networks with time-varying delays. Since there is a non-linearity in the leakage terms of stochastic Cohen–Grossberg neural networks, some techniques are needed to overcome the difficulty in dealing with the nonlinearity. By applying fixed points principle and Gronwall–Bellman inequality, some sufficient conditions on the existence and exponential stability of periodic solution for the stochastic neural networks are established. Moreover, a numerical example is presented to validate the theoretical results. Our results are also applicable to the existence and exponential stability of periodic solution for the corresponding deterministic systems.

中文翻译：

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具有时变时滞的随机Cohen-Grossberg神经网络的周期解

本文涉及具有时变时滞的一类随机Cohen-Grossberg神经网络的周期解。由于随机Cohen-Grossberg神经网络的泄漏项具有非线性，因此需要一些技术来克服处理非线性的困难。通过应用不动点原理和Gronwall-Bellman不等式，建立了关于随机神经网络周期解的存在性和指数稳定性的充分条件。此外，通过数值算例验证了理论结果。我们的结果也适用于相应确定性系统周期解的存在性和指数稳定性。