Stability Analysis Of A Class Of Recurrent Neural Networks With Proportional Delays

As a class of large-scale parallel processing dynamic system,which can deal with the data of nonlinear processing,recurrent neural networks with delays have attracted widely attention due to their potential in associative memories,pattern recognition,signal processing,optimization.Delay is objective existence,which may make the system lead to chaos.Proportional delays is a kind of delays,it's advantage that it can be convenient for us to control the network's running time according to the delays allowed by networks.Meanwhile this measure expand the application field of neural network.Therefore,the study of dynamic behaviors of recurrent neural networks with delays has important theoretical and practical value for circuit implementation and artificial simulation.This article discusses the stability of several proportional delayed recurrent neural networks.Firstly,the history of the development of recurrent neural networks,a brief introduction and current situation of delayed recurrent neural networks and proportional delayed recurrent neural networks were introduced in the introduction.Secondly,a class of second order Hopfield neural networks with proportional delays under impulsive perturbations was discussed.By constructing proper Lyapunov functional and applying inequality techniques,global exponential stability analysis for the given system is studied,and a delay-dependent sufficient condition for global exponential stability of equilibrium point of the system is obtained.Besides,these conditions provided a exponential convergence of the solution.Thirdly,global exponential stability analysis for a class of autonomous Cohen-Grossberg neural networks with proportional delay is studied.By applying Young inequality and constructing proper Lyapunov functional,a delay-independent condition for global exponential stability of the system is obtained.Fourthly,the global asymptotic stability for a class of cellular neural networks with multi-proportional delays is studied.Firstly,the existence of equilibrium the system is proved by the Brouwer fixed point theorem.Secondly,the uniqueness of equilibrium for the system is proved by the theory of matrix spectral radius.And then,by constructing proper Lyapunov functional and applying inequality analytic technique,combining with Barbalat lemma,the global asymptotic stability of the system is discussed,and two new delay-independent and delay-dependent sufficient conditions for global asymptotic stability of the system are obtained.Finally,a class of generalized cellular neural networks with multi-proportional delays is studied.At first,the existence and uniqueness of equilibrium of the system are certified by the Brouwer fixed point theorem.Then by establishing a delayed differential inequality,a delay-independent sufficient condition is obtained for guaranteeing the global exponential stability of equilibrium of the system.