Butterfly Catastrophe Model And Analysis Of Pest Population Dynamics

The core issue of population ecology is population dynamic. Population dynamicsstudies the controlled factors and mechanism of dynamic change in space and time ofpopulation quantity, structure and distribution, in order to describe the relationship among thelaw of changes, related physical factors and biological factors quantitatively. On the basis ofpopulation dynamic model, reasonable application of catastrophe theory to study populationdynamic can better explain the catastrophic phenomenon during the dynamic process ofpopulation quantity, which provides a new thought and method for the study of population.The large explosion of pests often brings great financial losses to the production ofagriculture and forestry. In the actual production of agriculture and forestry, it has greatsignificance to timely and accurately monitor and forecast the pest population quantity. Thecorrect simulation and forecast is a very important step to ensure the stable and highproduction of agriculture and forestry. The mathematical model has become an importantresearch method in ecology, in which the catastrophe theory model can describe the law ofchanges of system in equilibrium state when the external controlling factors change.Since the establishment of catastrophe theory, it was quickly applied into every applieddiscipline and successfully resolved a lot of troubles which cannot be resolved by other means.However, in previous studies, only one or two state variables were used to study thepopulation catastrophe which cannot be fully described. If there are three states of matter incatastrophe theory which could be transformed into each other reversibly, butterflycatastrophe model could be used to describe. And pest population quantity has three states ofmatter namely explosion, stabilization and reduction. These three can be transformed intoeach other, meaning that population quantity can transform from stabilization suddenexplosion, while it can also transform from explosion to sudden reduction. Therefore,higher-dimensional butterfly catastrophe model will be closer to actual in studying pest population dynamic and more favorable to the analysis of complex population dynamicpopulation dynamics.The main conclusions from this study are as follows:1. Based on the previous established pest population dynamic model, pesticides factor istaken into consideration. The pest population dynamic model, influenced by weather, cropconditions, pesticide and natural enemy, is built.2. With the theoretical basis of catastrophe theory, under the balance of pest populationdensity, butterfly catastrophe model of pest population density, influenced by weather, cropconditions, pesticide and natural enemy, is derived. In model, crop conditions, weather,pesticides and natural enemies of pests can be seen as4control variables, while the pestpopulation quantity dynamic as state variable.3. This study analyzes the equilibrium surface of butterfly catastrophe model andintuitively describes the five catastrophe characterizations in butterfly catastrophe system ofpest population.4. The study carries out catastrophe analysis on the butterfly catastrophe model of pestpopulation and determines the area in the system which may have catastrophe. It alsoanalyzes that in which area and under what kind of circumstances the catastrophe wouldhappen, which provides theoretical basis for pest control.