Stability analysis of stochastic reaction–diffusion neural networks with Markovian switching and time delays in the leakage terms

This paper investigates a class of stochastic reaction–diffusion neural networks with both Markovian jumping parameters and time delays in the leakage terms. By using the Lyapunov functional method, linear matrix inequality approach and stochastic analysis technique, a novel sufficient condition is derived to ensure the stochastic stability of the networks in the mean square sense. The proposed results, which do not require the differentiability and monotonicity of the activation functions, can be easily checked via Matlab LMI Toolbox. Moreover, they indicate that the stability behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results.