Adaptive Stabilizer Design of Reaction-Diffusion Neural Networks With Time-varying Delays

This paper is concerned with stabilization of a class of neural networks with both reaction-diffusion and time-varying delays, which is motivated under a practical consideration that diffusion effects can arise in neural network models such as when electrons are moving in asymmetric electromagnetic field. Firstly, a simple proof for the existence of equilibrium points of neural networks is revealed. Secondly, based on it, an adaptive control scheme is developed to ensure the global asymptotical stability of the targeted equilibrium point. Comparing to previous controller designs, the proposed stabilizer has a compact form and allows the system parameters to be unknown. Finally, we simulate spatio-temporal behaviors of two different (periodic and chaotic) reaction-diffusion neural networks with or without adaptive stabilizer.