Convergence analysis of the nontrivial stationary solution of the memristor-based neural networks with reaction-diffusion terms

This paper considers the convergence and existence problem for the nontivial stationary solution of a memristor-based neural network with reaction-diffusion(MNNs). We address the existence of the nontrivial stationary solution by investigating a compact operator whose fixed point is exactly the stationary solution through the Leary-Schauder theorem. Then, under some mild conditions, a lyapounov function is proposed to prove the convergence of the stationary solution. Numerial examples are provided to support the effectiveness of the conclusions.