Almost surely synchronization of directed coupled neural networks via stochastic distributed delayed impulsive control

This paper mainly focuses on studying the almost surely synchronization problem of directed coupled neural networks with time-varying delays. A new type of stochastic distributed impulsive controller is proposed to take impulse delays into account, where impulsive gains are assumed to obey the Gaussian distribution. By taking advantage of basic properties associated with graph theory, the Chebyshev inequality, the Borel–Cantelli Lemma and the Lyapunov functional method, some sufficient conditions for almost surely synchronization of delayed coupled impulsive neural networks with random impulsive gains are presented. Our result shows that, under the proposed stochastic impulsive control scheme, almost surely synchronization can be achieved even if the size of delays exceeds the length of impulsive intervals. Finally, two numerical examples are provided to verify the validity of the theoretical results.