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首页> 外文期刊>Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science >Analogies between urban hierarchies and river networks:Fractals, symmetry, and self-organized criticality
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Analogies between urban hierarchies and river networks:Fractals, symmetry, and self-organized criticality

机译：城市等级体系和河流网络之间的类比：分形，对称和自组织临界

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A pair of nonlinear programming models is built to explain the fractal structure of systems of cities and those of rivers. The hierarchies of cities can be characterized by a set of exponential functions, which is identical in form to the Horton–Strahler’s laws of the river networks. Four power laws can be derived from these exponential functions. The evolution of both systems of cities and rivers are then represented as nonlinear dual programming models: to maximize information entropy subject to a certain energy use or to minimize energy dissipation subject to certain information capacity. The optimal solutions of the programming problems are just the exponential equations associated with scaling relations. By doing so, fractals and the self-organized criticality marked by the power laws are interpreted using the idea from the entropy-maximization principle, which gives further weight to the suggestion that optimality of the system as a whole defines the dynamical origin of fractal forms in both nature and society.
机译：建立了一对非线性规划模型来解释城市和河流系统的分形结构。城市的层次结构可以通过一组指数函数来表征，这些函数的形式与霍顿–史特拉勒的河网定律相同。从这些指数函数可以得出四个幂定律。然后，将城市和河流系统的演化表示为非线性双重规划模型：最大化在一定能量使用下的信息熵或最小化特定信息容量下的能量消散。编程问题的最佳解决方案就是与比例关系相关的指数方程。通过这样做，使用熵最大化原理的思想来解释以幂定律标记的分形和自组织临界，这进一步证明了系统整体的最优性定义了分形形式的动力学起源的建议。在自然和社会中。

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