In this paper, we are concerned with a class of quaternion-valued stochastic neural networks with time-varying delays. Firstly, we cannot explicitly decompose the quaternion-valued stochastic systems into equivalent real-valued stochastic systems; by using the Banach fixed point theorem and stochastic analysis techniques, we obtain some sufficient conditions for the existence of square-mean pseudo almost periodic solutions for this class of neural networks. Then, by constructing an appropriate Lyapunov functional and stochastic analysis techniques, we can also obtain sufficient conditions for square-mean exponential stability of the considered neural networks. All of these results are new. Finally, two examples are given to illustrate the effectiveness and feasibility of our main results.

中文翻译：

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具有时变时滞的四元数随机神经网络的平方均值伪概周期解

在本文中，我们关注一类具有时变时滞的四元数值随机神经网络。首先，我们不能将四元数值随机系统显式分解为等效的实值随机系统；通过使用Banach不动点定理和随机分析技术，我们为此类神经网络获得了存在均方根伪几乎周期解的充分条件。然后，通过构建适当的Lyapunov函数和随机分析技术，我们还可以获得考虑的神经网络的平方均值指数稳定性的充分条件。所有这些结果都是新的。最后，给出两个例子来说明我们主要结果的有效性和可行性。