The Study Of Effects Of Delay And Impulse On Population Dynamical Systems

In this thesis, some theories and approaches related to continuous dynamics, discrete dynamics, impulsive dynamics, operator theory and numerical simulations are used to investigate dynamical behaviors including the existence and globally asymptotic stability of periodic solutions, permanence, extinction, and all kinds of complexities, and meanwhile the possible effects of delay and impulse on the dynamical behaviors are discussed. The whole thesis is devided into four chapters.The first chapter introduces concisely the historical situation and the present development of relevant subjects about population dynamics as well as the main work done in this thesis.In the second chapter, based on a general form of two types of well known periodic delayed single-species population growth models, we establish multiple delays competitive system, predator-prey system and facultative mutualism in 2.1, 2.2 and 2.3, respectively. By using Mawhin's continuous theorem and liapunov function, sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions of three systems are derived, respectively. These results show that sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions of non-autonomous periodic delayed systems formally correspond to that of positive equilibrium of autonomous undelayed systems, respectively. Moreover, these new results extend and improve some known results, and show that the periodic delays have the effects on the existence and globally asymptotic stability of positive periodic solutions. Biological interpretations and examples on the main results are also given.In the third chapter, according to the possible effect of periodic fluctuating environment and more than one past generation on the density-dependent population, we consider a discrete non-autonomous system of plankton allelopathy with delays and a discrete non-autonomous facultative mutualism system in 3.1 and 3.2, respectively. With the help of the properties of a Logistic single-species difference system, we obtain sufficient conditions for the permanence of the former system. By using Mawhin's...