Parasitic Wasp Control Larch Budmoth Population Model Stability Analysis And Numerical Simulation

This paper takes prevention and control of parasitic wasps on larch budmoth of the Alps as the research background. Through the establishment ofmathematical model of parasitic population, it analyzes feasibility of biologicalcontrol of forest pests, and studies complex dynamic behavior of parasiticdiscrete model through the method of numerical simulation. The major researchwork is as follows.In spite of the influence of plant quality on larch bud moth population, itestablishes tow models. They are two-dimensional parasitic model of parasiticwasps with functional response and two-dimensional parasitic model of parasiticwasps with self-limiting functional response. During this process, the functionalresponse of parasitic wasps and influence of self-limitation of parasitic wasps onthe population are taken into account. Based on relevant theories of differentialequation through mathematical proof, boundedness of the solutions of these twomodels, the stability of the boundary equilibrium point, as well as the sufficientcondition of uniqueness and stability of the existence of positive equilibriumpoint are obtained. Mathematical software is applied to the unique drawing ofexisting positive equilibrium point, which displays more intuitively the existenceuniqueness of positive equilibrium point.As the dynamic behaviors of these two models are rather complicated, thisessay thus applies the original experimental and Matlab software to the numericalsimulation. The numerical simulation is based on the combination of the researchresult of two types of mathematical models. It not only validates the correctnessof mathematical proof, but also observes the influence of every variable on themodel within different change scopes. Therefore, more dynamic behaviors ofmodel are gained. During the simulation process, the model shows phenomena ofperiodic oscillation, branch and chaos. An analysis based on simulation result shows that parasitic model of parasitic wasps with self-limiting functionalresponse is closer to the natural condition.