梯形映射族周期轨道的计算

运用符号动力学理论,研究一种特殊的一维分段线性映射族"梯形映射族"周期轨道的计算方法,确定其周期轨道的参数范围,给出了奇的最大周期序列对应参数的精确范围,以及偶的最大周期序列参数的近似范围.该方法可应用于更一般的单峰系统.     

二维对流扩散方程满足最大值原理的MMOCAA差分方法

Using FCT idea,the non-oscillation MMOCAA(The modified method of characteristics with adjusted advection) finite difference scheme satisfing the discrete maximum principle for convection-dominated diffusion equation in 2D is constructed.The scheme is free from oscillation,with which the problem is solved by the MMOCAA difference method based on 2-order Lag-range interpolation proposed by Jim.Douglas, Jr.(Numer.Math.,1999,83:353-369.). The error analysis of the new scheme and numerical example are given in the paper.The numerical example shows that the scheme has smaller numerical viscosity than the MMOCAA difference method based on bilineax Lagrange interpolation.     

DEVELOPMENT AND EVALUATION OF A SYSTEM DYNAMICS MODEL FOR INVESTIGATING AGRICULTURALLY DRIVEN LAND TRANSFORMATION IN THE NORTH CENTRAL UNITED STATES

Land transformation from grassland to cropland in the Northern Great Plains (NGP) has become a growing concern among many stakeholders. A growing body of work has sought to determine the amount and rate of land use change with less emphasis on the systemic structures or feedback processes of land use decisions. This paper presents the development of a system dynamics simulation model to integrate ecological, economic, and social components influencing land use decisions, including cattle ranching, cropland production, rural communities, land quality, and public policies. Evaluation indicated that the model satisfactorily predicted historical land, agricultural commodity, and rural community data from the model structure. Reference modes for key variables, including the farmland area, were characterized by a bias correction of 0.999, root mean squared error of prediction of 0.053, R² of 0.921, and concordance correlation coefficient of 0.0959. The model was robust under extreme and varying sensitivity tests, as well as adequately predicting land use under changing system context. The model's major contributions were the inclusion of decision‐making feedbacks from economic and social signals with connectivity to land quality and elasticity values that drive land transformation. Limitations include lack of spatial input and output capabilities useful for visual interfacing.