Nonnegative Periodic Dynamics Of Delayed Cohen-Grossberg Neural Networks With Discontinuous Activations

Since the emergence of MP model, the first artificial neural networks (ANNs) established by W.S.McCulloch and W.Pitts in 1943, the study of ANNs has been continued for sixty years. Many famous models have been proposed, including BP (back-propagation) neural network,ART (Adaptive Resonance Theory) neural net-work,Hopfield neural network, etc. In this dissertation, we study the nonnegative periodic dynamics of the delayed Cohen-Grossberg neural networks with discontinuous activation functions and periodic amplification function, self-inhibitions, interconnec-tion coefficients, and external inputs. The amplifier functions are assumed to satisfy certain conditions to guarantee the positivity of the solution. Also, the boundness of activation functions lies as an important role in the proof of the boundness of the solu-tion. Provided with fundamental knowledge of functional analysis, Filippov theory is utilized to study the viability, namely, the existence of the solution of the Cauchy prob-lem. Under some conditions, the existence and the asymptotical stability of a periodic solution are derived via Lyapunov functional method. Finally, numerical examples have been given to illustrate the theoretical results.