Application Of Impulsive Differential Equations In Population Control

Mathmatical models of differential equations play an important role in describing population dynamic behaviors. Mathmatically, these models explain all kinds of population dynamic behaviors, which allow people to understand population dynamics scientifically so that some interactions can be intended to control. Especially, impulsive differential equations describe population dynamic models, which more reasonable and precise on reflecting all kinds of change orderliness, Since many life phenimena and human exploitation are almost impulsive in the natural world. In this dissertation, we investigate the models with a fixed impulsive equation, two fixed impulsive equation and state-dependent impulsive eqution. By using the theories and methods of impulsive differential equations, we establish and study the dynamic models to aim at population control. At the same time, by using computer, we give the numerial simulation of all kinds of the dynamics of the models we study, including the stability of equilibrium, the existence of the periodic solutions, the permanence and extinction of system and the dynamics. The thesis is arranged by three chapters.In Chapter 1, the prey - predator model with a fixed Impulsive effect and Monod-Haldane function is studied. By using Floquet therem ,we obtain the condition that determined global asymptotic stability of pest-erdication periodic solution and permanence. The question of the nontrivial periodic solution off the round of pest-eradication periodic solution is discussed and the phenomenon of the pest-eradication periodic solution and the periodic outburst of pest are simulated by Matlab.In Chapter 2, considering biological control and chemical control strategies and the effect of chemical pesticides on natural enemies, we propose a prey - predator model with III functional response in two different time by using impulsive differential equation. It is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value . Otherwise, the system can be permanent. The question of the nontrivial periodic solution off the round of pest-eradication periodic solution is discussed and the phenomenon of the pest-eradication periodic solution and the periodic outburst of pest are simulated by Matlab.In Chapter 3, the prey - predator model with state-dependent Impulsive control and Holling III function is studied. By using the poincare map and the criterion of the poincare, we give the conditions that fold bifucation and flip bifucation occur. Moreover, we talk the existence and stability of positive periodic solution.