The Stability And Stability Analysis Of Several Types Of Recurrent Neural Networks With Proportional Delays

Recurrent neural networks are widely used in the fields of optimization design,pattern recog-nition,and data processing.Because in these applications,recurrent neural networks are required to meet certain dynamic properties,in addition,when the signal transmission process exists,delay causes chaos and instability in the system,therefore,it is of great significance to study the dy-namic properties of delay recurrent neural networks.Proportional delay is a kind of time-varying unbounded time delay,the significant advantage of proportional time delay neural network is that the operation time of the network is controlled according to the scale of proportional time delay factor and the maximum time delay allowed by the network.This paper focuses on the global asymptotic stability,global polynomial stabilization,global asymptotic stabilization and global polynomial stability of several types of recurrent neural networks with proportional delays.In the first chapter,the development history of recurrent neural networks,and the current research status of delay recurrent neural networks,the stability of neural networks with proportional delays,polynomial stabilization and polynomial stability of dynamical system are introduced.In the second chapter,Hopfield neural networks with proportional delay is studied,appropriate Lyapunov functionals and Barbalat lemma are used to study global asymptotic stability of the system,and two sufficient conditions for the global asymptotic stability of Hopfield neural network are obtained.In the third chapter,the concept of global polynomial stabilization of coupled neural networks with proportional delays was proposed.Firstly,the existence and uniqueness of the equilibrium point of the proposed coupled neural networks are proved by using homeomorphic mapping theorem.Secondly,by taking discrete controller,based on Lyapunov functionals and linear matrix inequality skills,we gain several delay-dependent global polynomial stabilization and global asymptotic stabi-lization criteria for the proposed system.The relationship among global polynomial stabilization,global exponential stabilization,and global asymptotic stabilization are also revealed.In the fourth chapter,the global polynomial stability of impulsive recurrent neural networks with proportional delays is investigated,constructing the Lyapunov functional method is not used,but the delay differential inequality method,the spectral radius of nonnegative matrices and the properties of M-cone,sufficient conditions of global polynomial stability of the equilibrium are given.The results obtained in this paper are new.Numerical examples and corresponding simula-tions are given in each chapter to verify the effectiveness and accuracy of the results.