| In this paper, we propose two classes of dynamical system in biology with impulsive effects. Based on the qualitative results of continuous dynamical models in biology, the managements of species are investigated by means of the theory of impulsive differential equations and numerical computing. The long-term managements can be investigated by discussing the effects of the impulse at fixed moments on the dynamical systems in biology and it will be useful for studying the dynamic complexity of ecosystems. The thesis has 4 chapters:Chapter 1 gives the biological backgrounds of the managements of species,briefly states the present studies of impulsive differential equation and its applications to the dynamical systems in biology.Chapter 2 introduces the basic theories and preliminaries of impulsive differential equation.In chapter 3, we analyzed a delayed stage-structured predator-prey model with Ivlev-type functional response, impulsively diffusive prey between patches and continuous harvesting on predator. By using a comparison theorem and the stroboscopic map of the discrete dynamical system,we obtain the globally attractive condition of predator-extinction periodic solution of the system, we also obtain the permanent condition of the system by theory of impulsive delay differential equation. Our results indicate that the effect of continuous harvesting predator plays an important role for the permanence of the system. Finally, a numerical analysis is given to show the effectiveness of the main results.In chapter 4, a food chain system with two impulsive perturbations is established. we show that this system is uniformly bounded. Using the Floquet theory of impulsive equations and small perturbation skills, we find conditions for the local stabilities of the prey and top predator-free periodic solution.Moreover, we obtain sufficient conditions for the system to be permanent via the comparison theorem. We display some numerical examples to substantiate our theoretical results. |
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