The Study Of Feedback Control And Impulsive Perturbation On Two Classes Of Almost Periodic Delay Competitive System

In this paper, considering the effect of almost periodic environment and delay on the population dynamics system we investigate a discrete almost periodic competitive system with feedback controls and delays, and an almost periodic impulsive differential system with delays, respectively. By using some correlative lemmas,theorems and constructing Lyapunov function, we obtain the existence and global asymptotic stability of almost periodic solutions for the above systems. Some examples and their corresponding numerical simulations are given at the end of each chapter. The entire article consists of three chapters:The first chapter introduces the background and research status of some difference equations, differential equations, and the effect of feedback controls,impulses, delays. We also review the history of almost periodic system, and introduce the main work in this thesis and some notations.In the second chapter, based on a class of two species competitive system, we consider its corresponding difference form together with the effect of feedback control variables and delays, and thus propose a discrete almost periodic competitive system with feedback controls and delays. By using the difference inequality comparison test,almost periodic functional hull theory and constructing Lyapunov function, sufficient conditions for the existence and global asymptotic stability of positive almost periodic solutions for the system are established. We also present specific numerical examples and corresponding numerical simulations to verify our theoretical results, and a summary ends the chapter.In the third chapter, considering the effect of linear impulse, we set up a delay almost periodic competitive system subject to impulsive perturbations. Through changing impulsive system into non-impulsive system, we derive the sufficient conditions ensuring that the system has a unique globally asymptotically stable positive almost periodic solution by application of differential inequality comparison test and the definition of asymptotically almost periodic function and constructing Lyapunov function. Several specific numerical examples and corresponding numerical simulations are used to verify our theoretical results, and a summary ends the chapter.In the fourth chapter, based on the results established of the second and third chapters, one makes a prospect for our future research, which including these work as follows: we can further study positive feedback control and more complex nonlinear feedback control according to the system in second chapter; as the extension of the work in the third chapter, we can also explore the impact of delay on intra-species term and different forms of delay. In addition, considering the effect of environmental noise, we can also establish stochastic difference model and stochastic differential model according to the systems in the second and third chapter..