Global Stability Analysis Of Recurrent Neural Networks With Proportional Delays

Recurrente nevrale netework(RNN)was widely use in image processing,combinatorial optimization,associative memory,pattern recognition and other fields because of its nonlinear mapping characteristics,associative storage function and self-organizing learning ability.The study of RNN has become a hot issue in artificial intelligence.The stability analysis of dynamic behavior of RNN system is the theoretical basis of its application,Therefore,it is of great theoretical and practical significance to study the stability of recurrent neural networks.Although the stability of neural networks has achieved fruitful research results,there are still many scientific problems to be solved in the theoretical research.This paper intends to use the methods of literature search and research,theoretical analysis,example calculation,simulation and numerical simulation,The stability of Hopfield neural networks with proportional delay,Hopfield neural networks with impulsive multi proportional delay,BAM neural networks with proportional delay and distributed delay are studied.In the first chapter,the research background and significance of neural network,the development process of neural network,the research status of recurrent neural network stability at home and abroad,the main research content and technical route of this paper are briefly summarized.In chapter 2,through the nonlinear transformation of Hopfield neural network with proportional delay,the system is replaced equivalently,and then the appropriate Lyapunov functional is constructed,and the relevant criteria for the global uniform asymptotic stability of Hopfield neural network are obtained.In Chapter 3,a sufficient condition for the global exponential stability of Hopfield neural network with impulsive multi proportional delay is obtained by nonlinear transformation,elimination of multi proportional delay and construction of suitable Lyapunov functional.In Chapter 4,the existence and uniqueness of the equilibrium point BAM neural network with proportional and distributed delays were proved by used the Banach contraction mapping principle.Then,the sufficient conditions for the global asymptotic stability of the BAM neural network are obtained by using Lyapunov functional and Young inequality techniques to obtain the global BAM neural network with proportional and distributed delays Sufficient conditions for asymptotic stability.In Chapter 2,Chapter 3 and Chapter 4,numerical examples were given respectively,and numerical simulations were carried out to verify the correctness and effectiveness of results.