Dynamic Analysis On Two Classes Of Functional Differential Equation Models

In recent years,the theory and application of functional differential equations have penetrated into various fields of natural and social sciences,especially the dynamics of functional differential equation models in the field of neural network dynamics and bioecol-ogy.Combining the methods of differential inequality,nonlinear functional?analysis and stability theory of functional differential equations,qualitative and stability problems of solutions for two kinds of non-autonomous functional differential equations are studied-One is shunting inhibitory cellular neural networks model with nonlinear decay function,and the other is Nicholson's blowflies model with nonlinear death density dependence function.The full text is divided into the following three chapters:In the first chapter,the development background and research status of the shunting inhibitory cellular neural networks model with nonlinear decay function and the Nichol-son's blowflies model with nonlinear death density dependence function are summarized.Then briefly state the main research contents and research ideas of this paper.Finally,the definitions needed in this paper and related preliminary lemma are listed.In the second chapter,the existence and stability of the asymptotic almost periodic solution of the shunting inhibitory cellular neural networks model with mixed time de-lay are studied in the asymptotic almost periodic environment.The proper Lyapunov function is constructed and the differential inequality technique is used.This method is combined with the basic properties of asymptotic almost periodic function,overcomes the nonlinearity of the model attenuation function,avoids the traditional exponential dichotomy theory,and we establishe some new criteria to guarantee the existence and asymptotic behavior of the solution of the model.Interestingly,we demonstrate that all solutions of the asymptotic almost periodic shunting inhibitory cellular neural network-s model converge to the same almost periodic function,and improve the corresponding results of some existing literatures.In addition,the validity of the theoretical results is verified by numerical simulation.In the third chapter,the positive,global existence,persistence,existence and sta-bility of the solutions for the Nicholson's blowflies model with nonlinear death density dependent functions are studied.In the case that the death density dependence function is D(x)=ax/b+x,by weakening the limitations of the existing literature,the new results of positive,global existence and persistence of solutions are established by the combination of differential inequality techniques and Dini derivative.And when the death density dependence function is D(x)?a-be-x,we establish the existence,uniqueness and exponential stability of positive periodic solution for Nicholson's blowflies model with continuous distributed delay by means of fluctuation lemma,Lyapunov functional and Dini derivative theory,which perfects the corresponding results of the existing literature.Finally,we give numerical examples of theoretical results.