Research On μ-stability And Synchronization Of Some Types Of Delayed Differential Equation

In recent years,the theory of differential equations and its related applications,which are derived from the fields of mathematics,engineering and physics,have leaded to the wide attention of great many researchers.Since time delays often occur in differential equations,which can lead to chaos in the system,and the existence of delay will have a certain impact on the dynamic characteristics of the system.Therefore,it is a practical subject to research the dynamic characteristics of delay differential equations.This dissertation mainly studies the μ-stability of Nicholson’s blowflies model with unbounded time-varying delay and the synchronization dynamics of two kinds of neural network systems with time delay.This thesis is divided into four chapters,and its research contents are organized as follows:In Chapter 1,the historical background and research progress of delay differential equations are summarized,and the research content of this article is briefly stated.Finally,the research significance and innovation of this paper are indicated.In Chapter 2,we mainly study a Nicholson’s blowflies model with unbounded time-varying delay,and establish a new criteria of the existence and μ-stability of the positive equilibrium of the model by using some new analytical techniques,which is a new dynamic characteristic of the considered model.The obtained results cover and extend some existing literature results.Finally,a numerical example is provided to support the correctness of the theoretical results.In Chapter 3,a kind of delayed memristive reaction-diffusion neural network system is further studied.By designing a novel exponential state feedback controller,using inequality techniques and finite time stability theory,a new criterion for finite-/fixed-time synchronization of the considered systems is established,which extends and supplements the results of the existing literature.Finally,a numerical simulation is given to verify the effectiveness of the theoretical consequence.In Chapter 4,the fixed-/preassigned-time synchronization problem of delayed inertial fuzzy Hopfield neural network with discontinuous activation function is mainly discussed.Firstly,by utilizing a new variable replacement,the original second-order model is turned into a first-order differential equation.Next,by designing a novel negative feedback controller and constructing a general Lyapunov functional,some new fixed time synchronization criteria of the model are established with the aid of the theory of Fillippov discontinuity and the upper bound for the settling time was estimated explicitly.Furthermore,according to similar mathematical derivation,the preassigned-time synchronization of the considered model is further studied,in which the settling time can be specified in advance and is independent of the initial value and any parameters.Figure [4] Table [0] Reference [78]...