The Research On Stability Of Several Random Neural Networks

The neural network has been developed for more than 60 years,it has been applied successfully in the fields of information and image processing,pattern recognition,associative memory and combinatorial optimization.It has also aroused wide attention of scholars at home and abroad.However,in neural networks,the occurrence of time delays is inevitable.The occurrence of time delays may affect the stability of the whole neural network.The stability theory of existing neural networks is mainly about the stability of neural networks with constant time delays and variable delays.Therefore,it is of great theoretical significance to study the stability of stochastic neural networks with time delays.The contents of this article are divided into four chapters.In the first chapter,we first introduce the history and research status of neural network,and then introduce the main contents and innovations of this paper.The second chapter introduces the theoretical knowledge of subsequent papers,including stochastic process,Brown motion,Ito formula and the definition of stability of stochastic differential equations.The third chapter studies the stability of stochastic Cohen-Grossberg neural network.By using inequality technique,martingale convergence theorem and Lyapunov function,a criterion for almost everywhere ?~r stability and the stability of P order?~rstability of Cohen-Grossberg neural networks with time delay is established,and almost everywhere exponential stability and P order moment exponent stability are its special cases.In the fourth chapter,we study the stability of stochastic fuzzy cellular neural networks.By using inequality technique,martingale convergence theorem and Lyapunov function,a criterion for almost everywhere?~rstability and P order?~r stability of a time-delay fuzzy cellular neural network is established,and almost everywhere exponential stability and P order moment exponent stability are its special cases.The last part is the summary of the thesis and the prospect of further research on stochastic neural network.