Synchronization in Quaternion-Valued Neural Networks with Delay and Stochastic Impulses

A class of global exponential synchronization problem for delayed quaternion-valued neural networks with stochastic impulses has been investigated in this paper, where the impulses arouse time and strength both are randomly. Firstly, the delayed quaternion-valued model with stochastic impulses was fain to separate to four real-valued parts in consideration of the fact that noncommutativity character of quaternion multiplication. Then, a new criterion was obtained to achieve the global exponential synchronization via building an appropriate classically Lyapunov candidate function and utilizing the method of comparison principle and reduction to absurdity. Finally, in order to verify the validity of the proposed theorem, a given numerical example is provided.