Study On The Permanence And Almost Periodic Solution For Three Classes Of Ecological Models With Feedback Controls

In population ecology,research on the dynamic properties of population models become an important content,and study on the population models with feedback control have attracted the attention of many mathematicians and biologists.This thesis mainly discusses three classes of population ecological models with feedback controls.Applied with different research methods,we obtain the sufficient conditions for the permanence,extinction,global attractivity of models and the uniformly asymptotically stability of a unique positive almost periodic solution of models respectively.Some new results have been presented.The research work of this thesis mainly includes:1.We investigate a nonautonomous discrete Schoner competitive system with saturated infectious force and feedback controls.By using the comparison theorems of difference equations,the mean value theorem and the valuation method,we obtain the sufficient conditions for the permanence,extinction and global attractivity of the system respectively.2.Through extending the classical Holling functional response function to general functional response function,we investigate a discrete almost periodic mixed system with feedback controls and predatoriness and competition of three species.By applying the comparison theorems of difference equation,mean value theorem and valuation methods,we obtain the sufficient conditions which guarantee the permanence and global attractability of the system.Moreover,by means of the theories of almost periodic function and constructing a suitable Lyapunov function,we obtain the sufficient conditions for the uniformly asymptotically stability of a unique positive almost periodic solution of the system.3.A class of Gilpin-Ayala ecological system with discrete and distributed time delays and feedback controls is concerned.Applying with the differential inequalities and detailed analysis,we obtain the sufficient conditions for the permanence of the system.Furthermore,using the properties of almost periodic function,Lyapunov method and the technique of some differential inequalities,we obtain the sufficient conditions for the existence of positive almost periodic solution of system.