Study On The Dynamics Of A Two Stage Structured Pest Control Filippov Model

With the developments in science and technology and the progress of the society, thepopulation management is based on the need of human development，agricultural productionand ecological aspects to regulate the number of one or some species in production practice.Especially, only when its quantity exceeds the economic injury level do we control pestpopulation. How to make the harmful insects and carriers cause minimum loss for humandisease, important plants and animals is always concerned by agricultural scientists. Therefore,the rapid development of Biomathematics is such that more and more of these aboveproblems can be researched by establishing an ecological mathematical model. In this paper,based on the non-smooth dynamical system, taking environmental pollution and the waste ofresources brought about by chemical pesticides into consideration, we establish a two stagestructured pest control Filippov model.In Chapter1, we introduce the background knowledge and development status.Concerning the most of pest population with stage structure, we introduce a single populationmodel with stage structure.In Chapter2, in order to fully study dynamic properties on stage structured pest controlFilippov model, this chapter gives the global analysis of continuous two stage structuredmodel with a Beverton-Holt birth rate function. First of all, we obtain the locallyasymptotically stable critical condition on the trivial equilibrium and positive equilibrium.local asymptotic stability of positive equilibrium point of critical condition; second, under theexistence condition of the positive equilibrium, we give the qualitative analysis of thehigh-order singular; finally, under the condition of locally asymptotic stability, we prove thetwo equilibriums are global asymptotically stable.In Chapter3, we take the quantity of the adults as the index for implementingchemical control strategies. In order to control the adult pest population so that itsdensity does not exceed economic threshold level, we establish a two stage structuredpest control Filippov model by using threshold policy control strategy and investigatethe dynamics of such a system systematically, including the sliding mode domain,existence and stability of regular equilibria, virtual equilibria and pseudo-equilibria, andthe bifurcation phenomena of the equilibria, tangent point and sliding mode.In Chapter4, we take the quantity of all the pests as the index for implementingchemical control strategies. By using threshold policy, the quantity of the adult and juvenile pest population does not exceed economic threshold level. We study morecomplex Filippov model and obtain much more dynamic properties. By numericsimulatio we give the locally bifurcation phenomena of the equilibria. We control allof the adu-lt and juvenile pest population on the economic threshold.Finally, we give an overall conclusion.