Abstract This paper concerns with the almost sure exponential synchronization for some general classes of drive-response stochastic memristive neural networks (SMNNs) with nonidentical nodes under state feedback controllers. The SMNNs considered may include networks which are asymmetrically nondelayed and delayed coupled simultaneously, and state-dependent or even those that are subject to exogenous stochastic perturbations representatively. The main results of this paper are a collection of generic sufficient conditions for guaranteed almost sure exponential synchronization of these SMNNs, which performs great advantages compared with mean-square synchronization. Furthermore, some practical corollaries are also obtained from the main results that may be directly applied to some smaller subclasses of these networks. In particular, a simpler and more effective way of almost surely exponentially synchronizing SMNNs without delays follows by considering them as a special case of SMNNs with delays. Some numerical simulations are given to illustrate our main theoretical findings.

中文翻译：

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驱动响应随机忆阻神经网络的几乎确定指数同步

摘要 本文涉及在状态反馈控制器下具有不同节点的某些一般类别的驱动响应随机忆阻神经网络 (SMNN) 的几乎确定的指数同步。所考虑的 SMNN 可能包括非对称非延迟和同时延迟耦合的网络，以及状态相关的网络，甚至那些典型地受到外生随机扰动的网络。本文的主要结果是为保证这些 SMNN 几乎确定的指数同步的通用充分条件的集合，与均方同步相比，它具有很大的优势。此外，还从主要结果中获得了一些实用的推论，这些推论可以直接应用于这些网络的一些较小的子类。特别是，一种更简单、更有效的方法几乎可以肯定地无延迟地以指数方式同步 SMNN，接下来将它们视为具有延迟的 SMNN 的特殊情况。给出了一些数值模拟来说明我们的主要理论发现。