Abstract
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.
Highlights
It is well known that the dynamic research on neural network models has achieved fruitful results, and it has been widely used in the fields of pattern recognition, automatic control, signal processing, and artificial intelligence
Stochastic neural network is an artificial neural network and is used as a tool of artificial intelligence. erefore, it is of practical importance to study the stochastic neural networks
To the best of our knowledge, up to now, there is no paper published on the existence and square-mean exponential stability for square-mean pseudo almost periodic solutions of quaternion-valued stochastic neural networks
Summary
It is well known that the dynamic research on neural network models has achieved fruitful results, and it has been widely used in the fields of pattern recognition, automatic control, signal processing, and artificial intelligence. To the best of our knowledge, up to now, there is no paper published on the existence and square-mean exponential stability for square-mean pseudo almost periodic solutions of quaternion-valued stochastic neural networks. It is a challenging and important problem in theories and applications. (1) Firstly, to the best of our knowledge, this is the first time to investigate the existence and square-mean exponential stability of square-mean pseudo almost periodic solutions for quaternion-valued stochastic delayed neural networks. (3) irdly, the techniques of this paper can be applied to study the square-mean pseudo almost periodic solutions for other types of quaternion-valued stochastic neural networks.
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