Dynamic Behaviors Of Several Classes Of Recurrent Neural Networks With Proportional Delays

Recurrent neural networks play an important role in pattern recognition,solving nonlinear constrained optimization,convex optimization real-time price problems and so on.The time delay is unavoidable in virtue of the finite switching speed of amplifiers in the process of inormation pro-cessing.And its existence has a marked impact on the dynamic behaviors of neural networks,and causes the emergence of some unstable phenomena such as periodic oscillation.periodic instability,bifurcation and so on.Proportional delay is a type of unbounded time-varying delay,this article discusses the dvnamic behaviors of several classes of recurrent.neural networks with proportional delays.In the first chapter,introduces the development history of recurrent neural networks,and the current research status of delayed recurrent neural networks,anti-periodic solutions of recurrent neural networks.passivity and synchronization of memristor-based recurrent neural networks.In the second chapter the global exponential stability of anti-periodic solutions of a class of cellular neural networks with proportional delays is discussed.By establishing appropriate delay differential inequalities,a sufficient condition is obtained to ensure the existeice and global exponential st.ability of anti-periodic solutions of the system.In the third chapter the passivity of memristor-based recurrent.neural networks with multi-proportional delays is investigated.We receive several new sufficient conditions for the passivity of nieniristor-based recurrent neural networks with multi-proportional delays,which are delay-independent and delay-dependent,by establishing appropriate Lyapunov functionals and utilizing inequality techniques.The criteria here are presented in the form of linear matrix inqualities.In the fourth chapter,the exponential synchronization of memristor-based recurrent neural networks with multi-proportional delays is investigated.We receive a delay-independent sufficient condition based on the theories of set-valued maps and differential incusions,by means of con-structing a Lyapunov functional as well as taking advantage of Young inequality.The conclusions obtained in this paper are new and an be validated by a simple algebraic operation easily.The corresponding numerical examples and their simulations are given in each chapter to illustrate the accuracy and effectiveness of the obtained results.The obtained results provide fundamental basis for concrete construction and realization of the recurrent neural net-works with proportional delays.