This paper is concerned with Hopfield neural networks with unbounded time-varying delay driven by G-Brownian motion. The existence and uniqueness of solutions, as well as the continuity of solutions in the sense of G-mean square, are investigated for such neural networks. Moreover, sufficient conditions dependent on delay are derived to guarantee G-mean square asymptotic stability and G-mean square exponential stability of neural networks. At last, two examples are provided to illustrate the application of the obtained results.

中文翻译：

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G-布朗运动驱动的无界时延Hopfield神经网络稳定性分析

本文关注的是由 G-Brownian 运动驱动的具有无界时变延迟的 Hopfield 神经网络。对于这种神经网络，研究了解的存在性和唯一性，以及 G 均方意义上的解的连续性。此外，推导出依赖于延迟的充分条件来保证神经网络的G均方渐近稳定性和G均方指数稳定性。最后给出了两个例子来说明所得结果的应用。