| In this paper, according to the integrated approach, which is qualitative and quantitative, some fundamental research on the complexity of the urban resource-environment system were done with the application of the Dissipative Structure Theory.The urban resource-environment system is a dissipative structure with the characteristics as follows: openness, far from equilibrium, complicated non-linear interaction within the system, fluctuation and abrupt change. According to the causes to the five types of entropy produces (component entropy, structural entropy, functional entropy, time entropy and environmental entropy) we can get that a city with the aim to sustainable development should act as follows: keeping far from equilibrium, enhancing the communication with the outside world, keeping positive reaction to changes, promoting dynamic cooperation and amplifying fluctuation selectively.In the field of quantitative simulation of the urban resource-environment system there have been two good models. The urban population model with a single variable can simulate the whole process that the city develops from a small one to a large one, and from an independent one to a higher grade one. The distributing structure model of American population can be used to simulate the situation of employment and unemployment in every state of the United States. The simulating results are considered more accurate than others by related experts and are admitted by American government so that the results are regarded as the reference for establishing new policy. On the base of the two models aforementioned the model system for control of coordinated development to the urban resource-environment system was brought forward in this paper, which described the system with only a few variables. The interaction within the system embodied by the model system made it possible to control the coordinated development to the urban resource-system. The result of its application reflected the real situation well.The super entropy produce criterion is a good tool to judge the system's abrupt change from a lower grade to a higher one. In this paper the entropy of the urban resource-environment system was defined, and in an example of its application thesuper entropy produce criterion of the urban resource-environment system reflected the real developmental process of the whole system. Furthermore, in this paper, A new model for the grid size optimization of the finite element method (applied to the water quality modeling of the topographically complicated river) was brought forward based on the maximum information entropy theory in condition that the length of gird was given. In a practical example, the optimized width of the grid was gained and the influence of some parameters was studied. The results demonstrated that the model reflected the real situation of the pollutants in river and had such characteristics as stabilization and credibility, which suggested the model has high applicability.Research on the complexity of the urban resource-environment system is fundamental at home and abroad. The work made in this paper is very coarse and not perfect. There is a will that this paper would bring forth much more researches. |