Research On The Dynamics Of Disturbed Ecological Environment Systems

Many biological phenomena cannot be described by continuous dynamics entirely. Impulsive differential equations are suitable for the mathematical modeling of evolutionary processes which experience a change of state abruptly owing to instantaneous perturbations. In this thesis, based on impulsive differential equations, it investigates a single species model and predator-prey model with Gompertz law of growth in a polluted environment with periodic pulse toxicant input, it constructs a pest control model and the effect of pesticide input in the environment and in the organism is considered, so the pollution model should be introduced. Finally, numerical simulations are used to investigate dynamical behaviors.In introduction, it introduces the research background and status of the population dynamic models which are investigated with impulsive differential equations and the major work in this paper.In chapter 1, it proposes a Gompertz predator-prey model in a polluted environment with impulsive toxicant input. The predator is age structure, the pest is catched or poisoned impulsively and the natural enemy amount is decreasing associated with the uptake of toxin. By using stability theory, comparison theorem and analytic method, sufficient conditions for the global attractiveness of the predator-extinction periodic solution and permanent are obtained. It is proved that the predator population can be eradicated totally when the pest population is catched or poisoned at a certain extent and the toxin input amount is too large. The numerical simulations verify the theoretical results.In chapter 2, it investigates a Gompertz single species model in a polluted environment with impulsive toxicant input an consider the effect of delay. The condition for the permanence of the system is given. It is shown that impulsive period and toxic input amount can bring obvious effects on the dynamics of system. The theoretical results are verified by numerical simulation.In chapter 3, it constructs a pest control model which is age structure for pest by introducing a constant periodic pesticide input and releasing natural enemies at different fixed moment. The pollution model is introduced to our model to describe the process of spraying pesticides. By using the stability of periodic solution and comparison theorem, the conditions for the permanence and the global attractiveness of the pest-extinction periodic solution are obtained.