Catastrophe Model For Pest Population Dynamics Under The Influence Of Climate Change

The French mathematician Rene Thom founded the mutation theory more than forty years ago,mainly for the study of some changes happen suddenly under the change of parameters are continuous and smooth.After its production,in many areas have a part of the application,used to study such as water gas and gas changes,earthquakes,volcanic eruptions,debris flows,desertification processes,car buying climax occurred,the development of sports capacity,the occurrence of plant diseases and pestsand other discontinuities or between the continuous and discontinuous phenomeno.Wheat is an important economic crop in the world,from planting to harvest at all stages often suffer from various pests and diseases.Aphids is one of the most serious pests causing the loss of yield,in the surrounding environment of the various factors of continuous smooth changes often outbreak on a sudden,if not controlled and prevented,will affect the normal growth of wheat caused by economic losses.Therefore,it is of great theoretical and practical significance to understand the aphid species under the natural conditions,not only to reduce the loss of wheat yield and quality caused by aphids,but also to study the pathogenesis of pests.Suppose that when the area of the study does not change,the wheat variety,the natural enemy situation,the farmers fertilize,spray pesticide changes in the interannual variation.The climatic factors were refined.In this study,the dynamic equation of aphids population was established by temperature,relative humidity and crop condition(environmental capacity)as control variables.The model was used to deduce the swallowtail mutation of aphids Standard form.With the help of the knowledge of mutation theory,the mutant analysis was carried out under the intervention of three external influencing factors of temperature,relative humidity and crop condition(environmental capacity),according to the actual data when the main discussion of the corresponding situation.The main conclusion is below:1?In this paper,we consider the generalized Logistic model,which changes the meteorological factors that describe the meteorological factors only by temperature and increase the relative humidity.It is more in line with the actual situation.The model of three factors was established by using temperature,relative humidity and crop condition(environmental capacity)as control variables.2?Based on the knowledge of mutation theory,the swallowtail mutation model under the combined effect of temperature,relative humidity and crop condition was deduced.The three control variables and one state variable in the swallowtail mutation model are influenced by temperature,relative humidity and crop condition.3?The points of divergence of the swallowtail are analyzed,and the possible situation of the control points in different regions may be studied: When aphids population dynamics in bifurcation ? area and to the four regions?,?,?,? changes,aphids population system will produce a mutation.When the control variable from ? area to ?,?,? area,the stability of the system does not cause catastrophe.When the control variable from ????? area to ? area,the stability of the system does not cause catastrophe too.4?Using the software OpenLu on the parameters,and the parameters of the fitting,with the software Opt function fitting.With the 1987 data for the relevant data validation,the effect is better.For the actual situation may occur mutations,given the corresponding explanation.And provide the theoretical basis for the ecological regulation of aphids.