Catastrophe Theory And Its Application In Ecological Regulation Of Pests

There are a lot of discontinuous changes in nature caused by continuous movements,such as volcanic eruption,earthquake,debris flow,bridge rupture,cell division,dog barking and so on.These kinds of phenomena are difficult to describe by the knowledge of calculus or statistics.However,the emergence of catastrophe theory provides a theoretical basis for the study of these phenomena.The catastrophe theory has been applied in various research fields since its inception,and it have made remarkable achievements on applications.Sudden outbreaks or disappearance of pests in agroecosystems also belongs to catastrophe phenomenon.It will bring heavy losses of agricultural production.However,the occurrence,development and catastrophe of pests involve many ecological factors such as natural factor,biological factor,social factor.It is very difficult to make accurate prediction.This is more difficult when multiple control variables and state variables are involved.The catastrophe models can be used to predict the significant and subtle changes of the state variables in the system,which can explain and predict the occurrence of the catastrophe——It is essential to practical management of pests in agroecosystem.Based on the catastrophe theory,this study analyzed the catastrophe phenomena of the arthropod community in kiwifruit orchards and aphids in the ecosystem.Because the models of fold catastrophe,cusp catastrophe,swallowtail catastrophe and butterfly catastrophe have only one state variable,and the study of two state variables catastrophe model,which is closer to the actual changes of ecosystem and can describe and reflect the changes of pest ecosystem better,is few.In this study,the elliptic,hyperbolic and parabolic umbilic catastrophe models are analyzed in detail by two unique methods(phase plane and potential function).The number of equilibrium points and the stability change of the system were obtained,which is the key of disaster prediction and dynamic control threshold.The purpose of this study is to provide a theoretical basis and forecast the regulation effect for the ecological regulation of pests,and to fill the gap of catastrophe theory and prediction.In this paper the results show that: 1.The expression of region division of bifurcation set of seven catastrophe models was derived.The conditions under which the catastrophe may occur were theoretically proved and explained.2.Based on the basic knowledge of ecology and catastrophe theory,the catastrophe mechanism of pest ecological regulation was studied,and a generalized wheat aphid population dynamic model based on catastrophe models was established.The dynamic threshold function for controlling the change of aphid population was obtained.The simulation of field survey data proved that the model can not only predict the outbreak of pests but also predict the effect of control measures.Therefore,the catastrophe model can provide scientific basis for explaining and predicting the outbreak scale and occurrence probability of aphids.3.Based on the generalized population dynamic model,a model of wheat aphids based on the cusp catastrophe model was established.We used field measured data to calculate the integrated control variables u and v.Then we determined the area where the control points located in the control panel,and analyzed the change of the position of the control points.It is proved that the bifurcation set of cusp catastrophe model is a quantitative dynamic control threshold,which can be used to explain and predict the outbreak of aphid population.4.By comparing the root mean square error(RMSE)of two methods,it is concluded that the RMSE of the two-stage method is smaller than that of the grey estimation method.The population dynamic catastrophe model of wheat aphid has the following advantages:(1)the population dynamic model pays more attention to the mechanism authenticity,system structure and function than the statistical model.That is,the population dynamic model can reflect the biological significance of the essential characteristics of the wheat aphid ecosystem.(2)the population dynamic model can be transformed into catastrophe models,which can be used to predict not only the general state of pest system(no catastrophe behavior)but also the occurrence of catastrophe behavior(outbreak of aphids).It can predict what will happen if some certain measures are taken.5.Two kinds of catastrophe models,elliptic umbilic catastrophe model and hyperbolic umbilic catastrophe model,were established by using principal component analysis.Then survey data of the arthropod community in kiwifruit orchard was analyzed.By comparing the results of the elliptic umbilic catastrophe model and hyperbolic umbilic catastrophe model,we found that the hyperbolic umbilic catastrophe model is more suitable for describing arthropod community in kiwifruit orchards than the elliptic umbilic catastrophe model.6.The necessary program for model fitting was designed.The catastrophe progression can be obtained by the self-defined function MYCCP,which provides a guarantee for the application of the model and reduces the difficulty.In summary: This research studies the catastrophe mechanism in the ecological regulation of arthropod population.We deduce the expression of region division of bifurcation set of seven catastrophe models,which can be used to judge whether the pest population will occur catastrophe.The possible catastrophe conditions were theoretically proved and explained.Then the generalized dynamic population dynamics of wheat aphids and the wheat aphid population dynamics model based on the cusp catastrophe model were established.The dynamic threshold function of controlling aphid population was obtained and tested by field experiment,which proved the superiority of catastrophe model in pest disaster prediction.We established two kinds of catastrophe models,elliptic umbilic catastrophe model and hyperbolic umbilic catastrophe model,and used them to analyze the arthropod community in kiwifruit orchard.It is proved that the hyperbolic umbilic catastrophe model can describe the arthropod community in kiwifruit orchard better than the elliptic umbilic catastrophe model.Although arthropod is the main object of this study,it can also be extended to the ecological regulation of any pests in agroecosystem.At the same time,this study will also fill the gap in the research and application of catastrophe models with high-order control variables.