不同氮水平下大豆与玉米单、间作氮素吸收的微分方程建模
Differential Equation Modeling of Nitrogen Uptake in Soybean and Maize Monoculture and Intercropping under Different Nitrogen Levels

大豆/玉米间作具有一定的养分利用优势，但是不同氮水平下的间作体系对氮素吸收的响应不同。在本文中，首先分别建立了自然条件下大豆和玉米单作氮素吸收的非自治Logistic微分方程模型，探讨了不同氮水平下大豆和玉米单作时氮素吸收的非自治Logistic微分方程模型，得到单作大豆和玉米的最佳施氮量分别为0.4808 g？plant^？1、2.6199 g？plant^？1。然后，进一步建立了不同氮水平下大豆和玉米间作氮素吸收的二维非自治微分方程模型，对模型拟合的相关系数均在98%以上，数值计算得到间作大豆和玉米的最佳施氮量分别为0.4821 g？plant^？1、2.6201 g？plant^？1，与单作结果差别不大，然而，两作物的氮素吸收量在不同氮水平交叉种植模式下却有着显著差异。在最佳施氮量下，间作玉米的氮素吸收量最大为4.48 g？plant^？1，较自然间作提升了59.43%，而大豆的氮素吸收量为1.31 g？plant^？1，较自然间作也提升了32.32%；就氮肥利用率而言，最佳施氮量下间作大豆相比最佳单作大豆下降了24.01%，而最佳间作玉米相比最佳单作玉米则提高了30.45%。
Soybean/corn intercropping has certain advantages in nutrient utilization, but the response of in-tercropping systems to nitrogen uptake is different under different nitrogen levels. In this paper, non-autonomous Logistic differential equation models of nitrogen absorption of monoculture soy-bean and corn under natural conditions were established respectively, and non-autonomous Lo-gistic differential equation models of nitrogen absorption of soybean and corn under different ni-trogen levels were discussed at first. The optimal nitrogen application rates for the soybean and maize were 0.4808 g？plant^？1 and 2.6199 g？plant^？1, respectively. Then, a two-dimensional non-autonomous differential equation model was established further for the nitrogen uptake be-tween soybean and corn at different nitrogen levels. The correlation coefficients of the model were all above 98%. The optimal nitrogen application rates for intercropping soybean and corn were 0.4821 g？plant？1 and 2.6201 g？plant^？1 respectively, which was no significant difference between the intercrops and monoculture results. However, the nitrogen uptake of the two crops was significantly different under different nitrogen levels of cross-cropping. Under the optimal nitrogen application rate, the maximum nitrogen uptake of intercropping maize was 4.48 g？plant^？1, which was 59.43% higher than that of natural intercropping, while the nitrogen uptake of soybean was 1.31 g？plant^？1, which was 32.32% higher than that of natural intercropping. In terms of the nitrogen utilization ra-tios, the best intercropping soybean decreased by 24.01% by comparing with the best monoculture soybean, while the best intercropping corn increased by 30.45% by comparing with the best mon-oculture corn.