Qualitative Analysis Of Several Classes Of Population Ecosystems With Feedback Control

Qualitative analysis of population model is an important research content of population ecology.Introducing feedback control variables into the population system to study the effects of feedback control variables on population dynamics behavior,which is beneficial to maintain the dynamic balance of the ecosystem.We mainly study three classes of population ecosystems with feedback controls,by using the qualitative and stability theory of differential equations,the theory of stochastic differential equations,the theory of almost periodic functions,the theory of time scale and methods.Some new results have been obtained:Firstly,a class of stochastic competitive system with single feedback control and nonlinear suppression term is studied.Using the comparative principle of stochastic differential equations,the generalized integral mean value theorem,the method of contradictory evidence and the It(?) formula,we get the sufficient conditions for the existence and uniqueness of the global positive solution of the system and the extinction of two groups and the extinction of a certain population,stability in the mean of another population,respectively.Secondly,a class of non-autonomous four species mixed system with higher-order nonlinear feedback control is studied.Applying differential inequalities and analytical skills obtains sufficient conditions for the persistence of three populations and the extinction of one population.Based on this,constructing a suitable Lyapunov function and applying Barbalat lemma,the sufficient condition of the global attractivity of the system is obtained.When one group extincts,we establish sufficient conditions for the uniformly asymptotically stability of a unique positive almost solutions of the corresponding subsystem of the system.Finally,an example is given to illustrate the feasibility of the result.Thirdly,a class of Schoner competitive system with feedback control and toxin on time scale is studied.Using differential inequalities,we can obtain the sufficient conditions for extinction of one population and the persistence of the another population of the system and the persistence of two populations,respectively.Moreover,when two populations are persistent,by constructing a suitable Lyapunov function and applying differential mean value theorem,the sufficient conditions for the existence and uniqueness and uniform asymptotic stability of positive almost periodic solutions are obtained.