Differential Equation Modeling Of Peanut Growth And Development In Three Different Environments

China is a large country of peanut production and consumption.The production of peanut is crucial to China's vegetable oil security.The production of peanut is affected by many factors,such as the root systems in growth,intercropping growth,and drought,so on.In this dissertation,based on the basic facts of peanuts' growth and Logistic differential equation model,differential equation models are established for describing the growth of peanuts in three different environments.Numerical simulation analysis is carried out.The concrete results are given as follows:Under the natural conditions,a differential equation model of monoculture peanut is established firstly.Then the sowing depth is as an influencing factor and added into the monoculture model.Numerical simulation results show that the dry matter accumulation of peanut is optimal when the sowing depth is 5cm.Furthermore,by considering the relationship between peanut's root length and dry matter accumulation,a two-dimensional differential equation model of peanut's root length and dry matter accumulation is established.Numerical simulation results of the model show that the dry matter accumulation is proportionate to peanut's root length.Under the condition of intercropping,a differential equation model is established for the intercropping of peanut and maize.Through theoretical analysis,the parameter conditions of the unique and stable positive equilibrium point of the intercropping model are obtained.Numerical results show that the dry matter accumulation of intercropping peanut is 54.01 which is 11.17% less than that of monoculture peanut,and that the dry matter accumulation of intercropping maize is 401.8 which is 14.8%higher than that of monoculture maize.Especially,the total dry matter accumulation of both peanut and maize increases by 11.15% under the condition of intercropping.Under the condition of drought,the relative water amount in soil is as an influence factor and added into the intercropping model of peanut and maize.Numerical simulation results of the intercropping model show that the dry matter accumulation of droughty peanut is 47.43 which is decreased by 13.2%,while the dry matter accumulation of droughty maize is 392.6 which is decreased by 2.3%.However,the total dry matter accumulation is increased by 7.12%,compared with the natural monoculture model.This implies that the intercropping peanut and maize could ensure drought resistance and increase the total dry matter accumulation.Under the condition of drought,the relative water amount in soil is as an influence factor and added into the monoculture models of peanut and maize,and the numerical simulations show that under the drought stress,the dry matter accumulation of monoculture peanut was 54.02,which is decreased by 11.2%,while the dry matter accumulation of monoculture maize was 346.2,which is decreased by 1%.This implies that the drought resistance of peanut monocropping is better than that of intercropping,but that of intercropping maize is better than that of monoculture maize.