The Stability Analysis Of Delayed Recurrent Neural Networks

Because of the existence of the feedback,the recurrent neural networks is a kind of nonlinear dynamic system,which is widely used in many fields,such as pattern recognition,signal processing,automatic,associative memories.As a dynamic system,all kinds of static models presented by neural system are the basis of a series of intelligent activities,such as the simulative study of biological neural system,the associative memories and the pattern recognition.Its stability is very important in dynamic systems.Therefore,the study of recurrent neural networks with delays has an important meaning in theory and practice.In the first chapter,introduces the recursive neural networks,the development of time-delay neural networks and its application prospect.Secondly,the recursive neural networks as well as the stability and periodicity of time-delay neural networks research present situation have carried on the simple introduction.In the second chapter,the exponential Stability of almost periodic solutions for cellular neural networks with proportional delay is studied.Without assuming the global Lipschitz conditions of output functions,a sufficient condition for the existence,uniqueness and exponential stability of almost periodic solution of the system are obtained by using the fixed point theorem and differential inequality technique.And two numerical examples are given to demonstrate the correctness of the conclusion.In the third chapter,the periodic solution of impulsive Hopfield neural networks with time-varying delay is studied.The output function satisfies Lipschitz condition,but is not necessarily continuous differentiable.We are not using the appropriate Lyapunov functional,but using iterative analysis and inequality techniques.A sufficient condition for the existence and uniform stability of periodic solution of the system is obtained.This condition is simple and easy to verify.A numerical example and its simulation are given to illustrate the correctness and effectiveness of the obtained results.In the fourth chapter,exponential stability of competitive neural networks with proportional delays is studied.The fixed point theorem is used to prove the existence and uniqueness of the equilibrium point of the proportion delay competitive neural networks.Inequality techniques are used to get the sufficient conditions for the exponential stability of the system equilibrium point.An example is given to illustrate the effectiveness of the result and the relevant results are also improved in this paper.Results in the paper are new.Some corresponding numerical simulations of them are given.These results for the application and implementation of a class of linear recursive neural networks provide a certain theoretical support.