Impact of Economic Development Model on the Fitting Effect of the Mathematical Model of Changes in Cultivated Land Resources

The mathematical model is often used for fitting the trend of changes in cultivated land resources in the land use planning, but the fitting effect is different in different study areas. In this paper, we take two geographically adjacent cities with great differences in the economic development model, Xinghua City and Jingjiang City, as the research object. Using logarithmic model (M1), Kuznets model (M2), logistic model (M3) and multivariate linear model ( M4), we fit the process of changes in cultivated land resources during the period 1980-2009, and compare the differences in the fitting effect between different models. In terms of the model fitting effect in Xinghua City, it is in the order of M3>M4>M1>M2, which is related to the fact that the local areas lay great emphasis on agricultural development, and pay close attention to ensuring the cultivated land area; in terms of the model fitting effect in Jingjiang City, it is in the order of M1>M3>M4>M2, and the deep-seated cause is that its development model is dominated by extended trade expansion, and the level of intensive land use is constantly improved. In addition, we discuss the multi-stage characteristics of changes in cultivated land resources, and propose a solution of using the same model to simulate in various phases. The research results in Jingjiang City show that the coefficient of determination in the first phase (R2=0.958) and the standard error (SE =0.261) are both better than those of the original model (R2=0.945，SE=0.312); the coefficient of determination in the second phase is slightly low (R2=0.851), but the standard error is greatly improved (SE=0.137). Compared with the research conclusions of other scholars, it can be believed that this method can better solve the problems that the scatter plot of logistic model presents wave-shape and the scatter plot of Kuznets model presents "M"-shape, in order to improve the applicability of mathematical models.