Research On Stability And Synchronization Of Two Kinds Of Delayed Network Models

In recent years,the theory and application of artificial or biological neural networks have attracted extensive attention of researchers in many areas of mathematics and engineering.As a kind of nonlinear dynamic system,neural network models can usually be described in the form of functional differential equation and partial differential equation,their information processing function are reflected in the dynamic characteristics,including such as stability and synchronization.Therefore,it is of great theoretical and practical significance to further study the dynamic properties of kinds of neural network models with delays.This thesis mainly studies the stability of delayed inertial neural networks with continuous activation functions and the finite time synchronization of neural networks with discontinuous activation functions.The full text is divided into five chapters,and its main contents are as follows:The first chapter mainly introduces the historical background,development status and latest research progress of neural networks,especially the theoretical and technical challenges brought by time delay、discontinuous activation and diffusion effects to the dynamics of neural networks,and briefly states the research significance and motivation of this paper.In Chapter 2,the exponential stability of a class of delayed inertial gene regulatory networks is studied by using non reduced order method、basic inequality technology and Lyapunov stability theory.Compared with the existing studies,the results of this chapter significantly reduce the computational complexity.At last,the rationality of the theoretical results is supported by numerical simulation.In Chapter 3,a kind of reaction-diffusion neural network model with discontinuous activation functions is proposed.By designing a novel controller,with the help of Filippov regularization technology and generalized finite-/-fixed time convergence theorem,a new conclusion of finite-/-fixed time synchronization of the studied model is established,and the settling time is exactly estimated.The obtained theoretical results generalize and improve the existing literature results,and the effectiveness of the theoretical analysis is verified by numerical simulation.In Chapter 4,a class of delayed Hopfield neural network model with discontinuous activation function is further considered.Without the help of the existing finite-/-fixed time convergence theorem,the new conclusion of finite time anti synchronization of the studied model is realized by developing new analysis techniques and designing a delay independent controller,the theoretical results of this chapter provide a new perspective for realizing the finite time synchronization process of neural networks.Figure [9] Reference [94]...