Stabilization of distributed parameter Hopfield neural networks based on operator spectral theory

In this paper, we analyze the stability of distributed Hopfield neural networks. Distributed parameter Hopfield neural networks model is established by PDEs so state space of the controlled system belongs infinity dimensions, which is different from ODEs and DAEs models. Reaction-Diffusion Hopfield neural networks model is a new class of net systems which exist widely in control science, intelligent computation, cells of neurology and biology mathematica. Most of papers about Hopfield neural networks apply average Lyapunov function and M-matrix theory to study stability. Now, we use operator spectral theory to obtain stability of the system, which does not need complex calculation. At last, we make some simulations verify our criterions.