| In this paper, we propose two classes of dynamical sysytem in biology based on fish catch and agricultural ecological management of integrared pest management problems. Based on the theories of impulsive differential equations, the managements of species are investigated by means of discrete and continuous dynamic system and impulsive effects. The long-term managements can be investigaged by discussing the impulse at fixed time. There are four chapters in this thesis.In chapter1, the significance of the thesis, the background and the recent works are introduced.In chapter2, the basic theories and preliminaries of impulsive differential equation are introduced.In chapter3, a pest management predator-prey model is disscused. In this model we considered impulsive transmitting on predators, chemical control on preys, preys have stage-sturcture and time delay. By using the comparison theorem of impulsive differential equation, sufficient conditions of the global attractivity of prey-extincting solution as well as persistent exitence of the system were obtained. Futher, we proved that if the impulsive releasing rate for nature enemy is within an appropriate range, the pest and nature enemy may coexist. At the same time, the population of pest can be controlled under the level of E(EIL). Finally, some numerical simulations are given to show the effectiveness of the impulsive transmitting on predators.In charper4, a two prey and one predator model which predators have stage-structure and preys have Gompertz increasing rate is discussed. By using the comparison theorem of impulsive differential equation and stroboscopic map of discrete dynamical system, sufficient conditions of global attractivity of the prey-extincting solution and persistent exitence of the system are obtained. The results provide reliable basis for practial pest mangement. Finally, some numerical simulations are given to substantiate our theoretical results. |
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