Study On The Model Of Holling â…¡ Pest-control With State-dependent

In recent years, people pay more attention to the problem of pest-control. Reasonabletheoretical analysis plays an important role to realistic control. For the actual problem of pestmanagement, we should neither eliminate the pests completely, nor allow abusing chemicalpesticides to kill the untargeted creature vastly and pollute the environment. The rapiddevelopment of mathematical biology has made more ecological problems can be analyzedand studied by establishing a mathematical model. Basing on impulsive differential dynamicsystem, this paper establishes a Holling â…¡ predator-prey model and researches the existenceand attractiveness of order one periodic solution under the condition of one and twostate-dependent control, and then we do some numerical simulations. For practical problems,this paper provides a theoretical basis for decision-making. The specific research content asfollows:The first chapter introduces the research background and gives the related preliminaries.In the second chapter, we consider the rationality of the pest management. When thenumber of pests attains to a certain economic critical value, we set up a state-dependent pestmanagement model by releasing the natural enemies and spraying pesticide to control theamount of pests below the economic harm level. We define the successor function by using acontinuous semi-dynamical system and the quality theory of differential equation, and discussthe existence and attractiveness of order one periodic solution.In the third chapter, we consider that the pest control should reduce the negative effect,the pollution to the environment and the waste of economy to optimize the effect of pestmanagement. We introduce two economic critical values and set up a state-dependent pestmanagement model. When the number of pests reaches low economic critical value, werelease the natural enemies to control the pests to reduce the damage to the environment as faras possible; when the number of pests reaches high economic critical value, we release thenatural enemies and spray pesticide simultaneously to control the amount of pest. Meanwhile,we discuss the existence and attractiveness of order one periodic solution.