The Study Of Dynamic Behaviors On Three Types Of Nonautonomous Almost Periodic Competitive Systems

In this paper, together with the population dynamics model and the relevanttheoretical knowledge of almost periodic equations, we investigate three kinds ofnonautonomous almost periodic competitive systems including differential system,difference system and impulsive differential system. Using some related theorems andlemmas and Lyapunov function method, the dynamic behaviors including permanence,existence and stability of almost periodic solutions for the above systems areestablished, respectively. Also, we present some examples and their correspondingnumerical simulations. The whole paper has been divided into four chapters.The first chapter introduces the application backgrounds and research status ofdifferential equations, difference equations and impulsive differential equations, andthe history of population ecology almost periodic systems as well as the main workdone in this thesis.In the second chapter, consider the effect of the almost periodic phenomenon, weestablish a nonautonomous almost periodic differential competitive system based on atwo-species differential competitive system. By using the differential inequality,module contains theorem and Lyapunov function method, sufficient conditions forpermanence, existence and global asymptotic stability of positive almost periodicsolutions for the system are obtained, respectively. At last, we give an example and itscorresponding numerical simulations for our main results.In the third chapter, based on the above nonautonomous almost periodicdifferential competitive system, and difference equations are better than thedifferential equations in some aspects of describing the population ecology models.We establish a nonautonomous almost periodic difference version. A goodunderstanding of the existence and uniformly asymptotic stability of unique positivealmost periodic solution for the system by applying related preliminary lemmas andLyapunov function method, moreover, we give an example and its correspondingnumerical simulations.In the fourth chapter, we introduce linear impulses into the model in secondchapter, and establish a nonautonomous almost periodic competitive system subject toimpulsive perturbations. By the comparison between the solutions of impulsivesystem and the corresponding non-impulsive system, and constructing Lyapunovfunction, sufficient conditions ensuring the uniformly asymptotic stability of uniquepositive almost periodic solution for the system are derived. At last, we present anexample and its corresponding numerical simulations.