Cusp Catastrophe Strophe Model For Aphid Population Dynamic Under The Influence Of Predator And Wheat Growth

Wheat is the second largest economic crop in China after rice.In the process of its growth,it is often affected by a variety of diseases and insect pests,among which wheat aphids have a particularly severe impact on wheat quality and yield.Since wheat aphids have a strong fertility and a short life cycle,the number does not change continuously under continuous and smooth changes of various factors in the environment,but it suddenly increases or decreases at certain times.Therefore,understanding the catastrophic laws of wheat aphid populations not only reduces the loss of wheat yield and quality caused by aphids,but also has important theoretical and practical significance for the study of the mechanism of pests.The catastrophe theory was founded by French mathematician R.Thom in 1972.Based on topology,it describes the phenomena of abrupt(discontinuous)changes in the state of the system due to the continuous change of certain variables,which makes up for the calculus.The application of deficiencies,its application has been throughout the physical,economic,social sciences and ecology and other fields.Most of the predecessors' researches used climate and natural enemies as control variables,and did not consider the effect of plant growth status on the number of aphids.The growth status and chemical substances of host plants had a very important effect on the number of aphids,among which the plant water content.It is one of the main factors that affect the number of locusts.In addition,the moisture content of plants is affected by climatic factors.In order to avoid the interaction between the plant moisture content and the climate,the natural enemies and plant growth(moisture content)were selected as influencing factors,and the sharp angle mutations of the dynamics of the aphid population were established.The model uses the survey data to analyze the actual abrupt changes in the number of aphids in the field to provide a theoretical basis for the ecological regulation of wheat aphids.The study yielded the following results:1.Improve the dynamic model of the number of wheat aphids under predecessors' natural enemies stress and increase the plant growth status factors,which is more in line withthe actual situation.Based on the plant growth status(moisture content)and natural enemies as control variables,a dynamic model of the number of wheat aphids affected by two factors was established.2.Using the relevant knowledge of the mutation theory,when the above model reaches a state of equilibrium,a sharp angle mutation model of the numerical dynamics of wheat aphids under the comprehensive influence of natural enemies and plant growth conditions is obtained through topological transformation.3.Divide the divergence region of the sharp-angle mutation model,and study the possible occurrence of the system when the control variable is in different regions.4.Using the opt function in the software OpenLu to perform parameter fitting on the parameters,and using the data in 2016 to verify the relevant data,the effect is good.For the sudden changes that may occur in actual situations,corresponding explanations have been given.It provides a theoretical basis for the ecological regulation of aphids and their treatment.