Asymptotic Behavior Of Nonautonomous Population Models With Impulsive Effects

Population ecology is one of the important subdisciplines in biomathematics, which mainly investigates dynamic behavior and reveals evolvement law of species over time by using the theory of differential equation and linear algebra. Through a mass of observation, experiment and hypothesis, people build reasonable models of differential equations to simulate the realistic evolvement law of species to supply scientific guidance for protecting endangered species or raising productivity. In particular, research on the periodicity, permanence and asymptotical stability of species has important academic value and practical significance, and is the main content of asymptotical behavior.In recent years, the asymptotical behavior of continuous population models has been extensively studied, but species may often undergo short time rapid variation such as stocking and harvesting in real world. These phenomenons are not suitable treated as continuous models, and need to be studied by impulsive differential equations. In addition, noticing the universality of time delays in population, for the generality and universality, this thesis is devoted to asymptotic behavior of several nonautonomous population models with impulsive effects. The thesis, which comprises six chapters, is organized as follows.In the first chapter, we introduce the background and significance of topics, related theories of population ecology, several foundational models in population ecology, and some preliminary results and definitions.Chapters2and3treat two kinds of ratio-dependent predator-prey models with impulses and time delays. By using comparison theorem of impulsive differential equations, differential inequalities, and the permanence of single-species Kolmogorov impulsive systems, sufficient conditions which guarantee the permanence of Gause-type ratio-dependent predator-prey systems and Leslie-type ratio-dependent predator-prey systems are established, respectively. In addition, in chapter3, the global asymptotical stability of Leslie-type ratio-dependent predator-prey systems is also investigated.Chapters4and5deal with ratio-dependent predator-prey dispersion systems and Kolmogorov mutualism systems with impulses and time delays. By using the continuation theorem in coincidence degree theory, the sufficient criteria of the existence of positive periodic solutions are obtained, respectively.Our research results show that the time delays have no effects on the periodicity and permanence of the population systems but in contrast on the asymptotical stability of the population systems; the impulses have no effects on the asymptotical stability of the population systems but in contrast on the periodicity and permanence of the population systems.The models we studied are general, including the most celebrated prey growth types and functional responses. As corollaries, some applications are given. In particular, our results generalize or improve some known ones.Finally, in the last chapter, we generalize and discuss the results derived in this thesis.