Study On Several Nonautonomous Nonlinear Population Dynamics Systems

In this paper, we consider four kinds of nonautonomous nonlinear populationdynamics systems:Firstly, a general nonautonomous nonlinear two species predator-prey system isstudied. By applying some subtle analysis, some new sufficient conditions areobtained for guaranteeing the permanence of the system.Secondly, a general nonautonomous nonlinear multiple species prey-competitionsystem with infinite and discrete delays is studied. By using a lemma about nonlineardifferential inequality equation which is obtained in chapter1(Lemma1.2.5) andsome subtle analysis, sufficient conditions are obtained for guaranteeing thepermanence of the system. Our results improve and extend some in the literature.Thirdly, a nonautonomous nonlinear two species periodic competition systemwith infinite delay and diffusion is studied. By using the method of coincidencedegree, sufficient conditions are obtained for guaranteeing the system at least has apositive periodic solution.Fourthly, a nonautonomous nonlinear multiple species competition system withfinite continuous delays and feedback controls is studied. First of all, consideringgeneral nonautonomous system, by using a lemma about nonlinear differentialinequality equation which is obtained in chapter1(Lemma1.2.5), we obtain sufficientconditions for the permanence of the system and by constructing a suitable Lyapunovfunctional, we obtain sufficient conditions for the global attractivity of any positivesolution. Then, we consider almost periodic systems, by using the Razumikhin typetheorem, sufficient conditions are obtained for guaranteeing the system has only oneglobally stable positive almost periodic solution.