Convergence Of Nicholson’s Blowflies Model And Inertial Cohen-Grossberg Neural Networks With Time Delays

In recent years,the theory of delay differential equations has been widely used in the fields of physics,economics and biomathematics,especially in practical problems such as population ecology,epidemiology and neural network dynamics.Studying the dy namic behaviors(for example,the stability of periodic solutions,the attraction of equilibrium points and chaos,etc.)of delay differential equation models with practical application background has become an important topic for scholars at home and abroad.Through using the Lyapunov functional method,the basic theory of delay differential equations and the differential inequality techniques,this dissertation systematically studies the convergence of a class of Nicholson’s blowflies model involving multiple pairs of different time-varying delays and a class of inertial Cohen-Grossberg neural networks incorporating distributed delays,and the conclusions obtained in this paper improve and generalize the related results of the existing literatures.The full text is divided into the following four chapters:In Chapter 1,the historical background.development and research significance of two types of models are presented.The work to be studied in this paper is briefly explained,and the basic marks and lemmas needed in this paper are listed.In Chapter 2,assuming that the per capita daily adult mortality term is oscillating,we study the convergence for a patch structure Nicholson’s blowflies system involving an oscillating death rate and distinctive time-varying maturation and incubation delays.First of all,the positivity and global existence of the addressed system are proved by using concise mathematical analysis proof.Then,based on the differential inequality techniques,some sufficient criteria are established to guarantee the global exponential convergence of the zero equilibrium point for the studied model,which improve and perfect some relevant conclusions in the existing literature.Furthermore,the effectiveness and feasibility of the theoretical analysis are demonstrated by some numerical simulations.In Chapter 3,anti-periodicity on inertial Cohen-Grossberg neural networks incorporating distributed delays is explored.Firstly,to avoid the huge amount of calculation brought by the reduced-order method,one can verify that the solutions of the addressed system are exponentially attractive to each other by exploiting Lyapunov functional method.Secondly,with the help of differential inequality techniques and mathematical analysis skills,some sufficient conditions are demonstrated to guarantee the existence and global exponential stability of anti-periodic solutions for the addressed networks.Lastly,a simulation example is provided to illustrate the correctness of the theoretical findings.Finally,we summarize the research work and look forward to the future research fields.