With the development of global changes, researchers from all over the world attach attention to land use changes increasingly, and large scale land use changes which have resulted from urban expansion catch people’s eyes. In this paper, urban expansion and their spatial and temporal variability of the Beijing city has been studied over a period of 21 years (1984–2005) via statistical classification approaches based on the remotely sensed images obtained from sensors both Landsat TM5 and SPOT4. The research method includes three parts: First, using multi-temporal images, land use/land cover change is detected by means of remote sensing. Then, based on result of classification images, the process of land use/land cover change and the model of urban expansion are analyzed by GIS technologies. It includes markov and transfer matrix, trajectories analysis, the spatial distribution rules of urban land and the spatial distribution rules of urban expansion intensity. Concretely, these include Markov and transitional probabilities matrix and the spatial distribution rules of urban land and urban expansion intensity. Finally, the relationship of population, GDP and urban land area are built up through a linear regression analysis. Research shows that: 1) Land use/land cover change detection using multitemporal images by means of remote sensing and ration research of model of urban expansion by GIS are good means of research of urban expansion. 2) Research of time sequence land use / land cover change through analysis of urban expansion trajectories and index reveals of urban distribution rules in terms of spatial-temporal. 3) Combined the analysis of social economic data, the simulation of expansion urban land is given in amount. 1.

The relation between city and ecological environment forms in the coupling process of urban systems and environmental factors, in which there is a definite rule. Urban competitiveness embodies the evolvement and development of the city, using the dissipative structure principle and mathematical analysis, this paper probes into the coupling rule between urban competitiveness and ecological environment. It is indicated that the amicability degree of human environmental behavior determines the shape of environmental Kuznets curve, the human amicable behavior and technological progress are significant for coordinating the city development and improving the urban competitiveness.