Input-to-state stability of delayed reaction-diffusion neural networks with multiple impulses

This paper concerns the input-to-state stability problem of delayed reaction-diffusion neural networks with multiple impulses. After reformulating the neural-network model in term of an abstract impulsive functional differential equation, the criteria of input-to-state stability are established by the direct estimate of mild solution and an integral inequality with infinite distributed delay. It shows that the input-to-state stability of the continuous dynamics can be retained under certain multiple impulsive disturbance and the unstable continuous dynamics can be stabilised by the multiple impulsive control, if the intervals between the multiple impulses are bounded. The numerical simulation of two examples is given to show the effectiveness of theoretical results.