城市系统复杂性的数学描述初探

MATH CHARACTERIZATION OF THE COMPLEXITY OF URBAN SYSTEM

从城市巨系统构成、发展演化过程、与外部环境的关联等层面分析城市系统的复杂性,分析人—社会系统与城市系统本质联系,指出城市系统复杂性的基本特征。由于城市系统中存在着多样的复杂性,其研究方法也具有多样性。通过分析城市系统的位置变量和状态变量,借鉴和运用动力学系统中哈密顿方程、刘维定理等方法,来刻画城市系统运行中相对稳定的子系统和某些层面演化的复杂性。城市本质上不是一个可积系统,而是动态的非平衡的开放系统,系统通过不断地与外界交换物质、能量、信息来维持其结构的稳定性和有序状态。在城市内部扰动与外部扰动之间的共振作用下,城市中形成了大大小小的混沌的非线性的区域,表现出有序与无序共同作用,确定性与随机性、必然性与偶然性等多层面统一的动态特征。

The paper analyzes the complexity of urban system from the aspects such as urban huge system＇s composing,evolution process and relation with exterior circumstance,etc.Beeause there are various complexities in urban system, the researching ways are also various. It depicts the complexity of the relatively stable subsystem and some aspects＇ evolution in urban system＇s running by analyzing position variable and estate variable and using the dynamic system＇s Hamiltonian systems and Liouville＇s theorem for reference. And it forms big and small chaos region which is non-linear under the resonance effect between urban inner and exterior disorder.