Asymptotically Almost Periodicity On Nicholson's Blowflies Systems With Patch Structure And Nonlinear Density-dependent Mortality Terms

With the rapid progress of science and technology,mathematical models are being used more and more widely in various fields,especially in the fields of population ecology,epidemiology and neural network dynamics.Since the development and change of many things depend not only on the current state,but also on the past history state,the mathematical models described by delay differential equation can describe the development state of things more accurately.In recent years,the theoretical research of delay differential equations has made great progress,and has been applied to various fields of social science and natural science.In this thesis,we consider a special delayed population model–Nicholson's blowflies systems with patch structure and nonlinear density-dependent mortality terms.By using the basic theory of delay differential equation,differential inequality technique,and Lyapunov functional method,the existence and convergence of asymptotically almost periodic solutions of the model are studied.Moreover,we establish some criteria to guarantee the global exponential stability of the asymptotically almost periodic solutions of the system in an asymptotically almost periodic environment.The validity and sufficiency of the obtained results are illustrated by some numerical examples.The dissertation consists of three chapters.The main contents are as follows.In chapter 1,the research background and status quo,research aim and significance of the Nicholson's blowflies systems with patch structure and nonlinear densitydependent mortality terms are introduced.In chapter 2,the basic notation,concepts and related lemmas are listed.In chapter 3,by applying the differential inequality technique and Lyapunov functional method,some conditions for the existence,uniqueness and exponential stability of asymptotic almost periodic solutions for the Nicholson's blowflies with patch structure and nonlinear density-dependent mortality terms are established.Moreover,the correctness of the theoretical results is verified by an example and numerical simulation.