Two Catastrophe Model And Its Research Application In The Study Of Population Dynamics Of Pests

Aphid is one of the most important pests of winter wheat in China, with highreproduction rate and short life cycle (Pest2000). It can cause serious damage to agricultureby ingesting phloem sap, transmitting viruses. Depending on the chemical pesticides not onlydamages balance the environment and agriculture ecological system, but also leading tooutbreak of the secondary pests and pest resistance. in order to reduce and avoid the seriousyield loss that aphid brings, the agricultural production adopt the integrated ecologicalmanagements such as the insect to control insectIt is well known that the pest ecological control is based on the population dynamics. Inorder to predict the rise or the reduce of the population and provide the theoretical evidence,the previous studies process a lot of observations and lab researches, thereby building somepopulation dynamic models including differential equation, probability theory andstatistical theory. However, these models can only be used to describe continuous changingprocess of population dynamics while cannot describe the sudden condition of naturalconditions, such as earthquake, volcanic eruption and the pest outbreak and disappearedsuddenly. Although there are obvious advantage to describe the population catastrophe in thecatastrophe model, the current model still has the disadvantages, such as hard choice of thecontrol variable, parameter estimation, potential function and control variable interaction, torestrict the use of the catastrophe modelBasing on three control variable of the comprehensive climate factor, the biomass of thecrop and comprehensive enemy and the state variable of aphid population, this study build thecusp model and swallow model of aphid population, analyze the practice mutation principleof the field aphid population, solve the control variable and parameter estimation ofcatastrophe model, thereby providing the theoretical evidence of the pest integratedmanagement with the ecological control.Conclusions were drawn as the following:1. Principle component analysis and factor analysis were conducted for the controlvariables such as climate factor (temperature, precipitation, humidity and illumination time), natural enemies (lady beetle, hoverfly, spider and lacewing fly etc.), which could affectaphids population dynamics. And the synthetic climate control variable and the naturalenemies control variable influencing aphids population dynamics were obtained.2. The aphids population dynamic equation including the effects of climate factor andnatural enemies were established. And the cusp catastrophe model was founded based on theequation. What’s more, the cusp catastrophe model was applied and analyzed in actualcondition. The bifurcation set of the cusp catastrophe was divided into three parts. Byanalyzing the different amount of equilibrium points when control point go through thebifurcation set curved surface, the system stability of ecosystem was analyzed and therequirement of catastrophe in aphids population was found. the result of application indicatedthat the cusp catastrophe model could almost illustrate the catastrophe of aphids population.3. The catastrophe condition of aphids population was analyzed with the swallowcatastrophe model based on data. The bifurcation set were divided into five parts. The systemstability was analyzed and the requirement of aphids population catastrophe were found byanalyzing the different amount of equilibrium points when control point passing thebifurcation set curved surface. And the result was analyzed and checked in actual condition.What’s more, we analyzed and checked it according to the actual conditions. Though theresult of application indicated that the swallow catastrophe model could almost illustrate thecatastrophe of aphids population, the accuracy of the swallow catastrophe model is lowerthan that of the cusp catastrophe. Further study is needed for the reason.4. The method for parameters estimation was found. And we estimated the unknownparameters of the two models by using the method based on the gray system theory.Moreover, the result indicated that the method is reasonable.