Dynamic Behavior Analysis Of Neutral-type Neural Networks With Delay

Neural network model is a designed and synthesized simulation system in recent years to describe the transmission and processing of information between neurons in neural networks.In recent years,a variety of neural network models have been studied by scholars from all over the world.In practical application,time delays and uncertain parameters have affected the dynamic properties of neural network systems to some extent.Therefore,it is of great practical significance to study the dynamic properties of neural network models with time delay.In this paper,the stability and Hopf bifurcat io n of two kinds of neutral-type neural networks with different delays are involved in.In this paper,the dynamical behavior of neutral-type neural networks with time delays is carefully studied,and the stability of equilibrium point of neutral-type neural networks with single delay and the conditions for generating Hopf bifurcation are discussed and derived.Furthermore,the stability of the equilibrium point of neutral neural networks with two delays and the conditions for local Hopf bifurcation are also studied.What's more,by using the global Hopf bifurcation theorem,the existence of global periodic solutions is derived.The main contents of this paper are as follows:Firstly,the dynamic behavior of neutral-type differential equations with single delay is analyzed.By choosing appropriate Lyapunov function,the global asymptotic stabilit y of the equilibrium point of the neutral neural network differential equation with single delay is studied,and the sufficient conditions are derived.For the convenience of calculation,the equation is simplified to a linear equation,and the existence of Hopf bifurcation is obtained by using the knowledge of the existence of root of characterist ic equation.In addition,by using perturbation theory,the vibration expansion of any order is obtained according to the fundamental frequency coefficient,and the second-order frequency-amplitude relation is deduced in detail.Secondly,the dynamic behavior of neutral-type neural network different ia l equations with two delays is analyzed.Taking delays?₁ and?₂ as parameters separately,the local stability of the equilibrium point of the equation is discussed,and the sufficient conditions for the asymptotic stability of the system are derived.By using the central manifold theorem and normal form method,the conditions for Hopf bifurcat io n are obtained,and the formulas for the stability of periodic solutions and the direction of Hopf bifurcation are given.Moreover,the existence of the global periodic solution of the system is presented by using the global Hopf bifurcation theorem.Furthermore,the numerical simulation analysis is carried out for verifying the conclusions obtained from the previous analysis.Finally,the main work of the thesis is summarized in detail,and the future research topic and work are prospected.