Differential Equation Modeling Of Nitrogen Nutrient Absorption Of Soybean And Maize In Their Mono-and Intercroppings

In this dissertation,based on some basic facts in agriculture and the growth and development laws of soybean and corn,and reasonable assumptions,a logistic model of dry matter accumulation of monocropping soybean and maize at different nitrogen supply levels,a differential equation model of nitrogen uptake under monocropping and intercropping of soybean and maize,a differential equation model of nitrogen uptake and root length relationship between monocropping soybean and maize are established,respectivly.The specific results are obtained as follows:Firstly,a Logistic model of dry matter accumulation of monocropping soybean and maize is established.Then by adding the nitrogen application rate as an influencing factor to the model,a Logistic model of dry matter accumulation of monocropping soybean and maize at different nitrogen supply levels is established.Numerical simulation analysis shows that the optimal nitrogen application rate for the monocropping soybean is 0.41g/plant,and the optimal nitrogen application rate for the monocropping maize is 2.5g/plant.Secondly,a Logistic model of nitrogen uptake under monocropping of soybean and maize(called monocropping model)is established.Numerical simulation analysis shows that an appropriate amount of nitrogen fertilizer added before pod stage of the monocropping soybeanan could meet its nitrogen demand from pod stage to drum stage,while an appropriate amount of nitrogen fertilizer need to be added for the monocropping maize during its spinning stage.Furthermore,a differential equation system model for the nitrogen uptake under intercropping of soybean and maize(called intercropping model)is established.By selecting appropriate parameters in the intercropping model,it is proved theoretically that the unique positive equilibrium point of the intercropping model is stable(A discriminating method is given by using the signs of the elements of Jacobi matrix at the equalibrium point)and the intercropping have advantages.Numerical simulation analysis shows that the nitrogen absorption of intercropping maize is 4.29 g/plant,which is an increase of 20.17%compared with the monocropping maize;while the nitrogen absorption of intercropping soybean is 1.24g/plant,which is 26.19% less than that of the monocropping soybean.The total nitrogen uptake of both intercropping soybean and maize increases by 5.33%.which indicates that intercropping produces the advantage of nitrogen uptake.Finally,a two-dimensional differential equation system model is established for the relationship between root length and nitrogen uptake of monocropping soybean and maize.Numerical simulation analysis shows that both the root lengths of the monocropping soybean and maize have positive correlationship with their nitrogen uptake respectively by the way of concave curve.That the nitrogen absorption increases with the increase of root length is because the absorption area of the root length enlarges make the nitrogen absorption increase much so as to increase the root length more.