Stability And Hopf Bifurcation Analysis Of A Delayed Complex-valued Neural Network

The rapid development of technology has brought people's lives to a high and sharp age,especially the emergence of artificial intelligence has greatly improved the living standards of people in recent years.The artificial neural network plays an important role in the research of artificial intelligence.The structure and function of the biological brain are very complex,which dominates the whole human nervous system.The artificial neural network mainly studies how to imitate and execute some intelligent functions of human brain by machine,and develops relevant theories and techniques to serve people's production and life.Nowadays,it is widely used in many aspects,such as signal processing,speech recognition,water conservancy engineering,computer vision and so on.In this paper,we analyze the bifurcation behavior of a class of delayed complex valued neural network,and get the condition and direction of Hopf bifurcation.This paper mainly consists of three parts:In the first part,we make a comprehensive description of some basic knowledge which should be used in the article,including the stability theory of the ordinary differential equation,the Routh-Hurwitz criterion,the concept of delay differential equation and the condition of Hopf bifurcation.In the second part,we divide the activation function and the connection weights into their real parts and imaginary parts,and then consider the time delay ? as a bifurcation parameter,so the asymptotic stability,bifurcation and instability of the network are obtained by using the property of the root of the characteristic equation.In the last part,we first translate the system into functional differential equation,and then we obtain the direction of Hopf bifurcation by using normal form theory and center manifold theorem.In order to verify the above two conclusions,we carry out the numerical simulations of the system by matlab,and illustrate the correctness of the results.In addition,a simple numerical simulation is carried out for different parameters,and the different dynamic behaviors of the system are obtained.