自然与社会中的城市混沌与置换动力学
Urban chaos and replacement dynamics in nature and society
摘要：
自然界和社会中的许多生长现象都可以用S形函数来预测。城市化水平的增长曲线是典型的S型曲线，可以用Logistic函数来描述。Logistic模型隐含着一个置换过程，而Logistic置换则隐含着分岔和混沌等非线性动力学行为。通过数学变换和数值计算，我们可以证明一维映射是由二维两群相互作用映射而来的。本文通过与城市化的类比，提出了置换动力学的一般理论，并利用二维图模拟了置换过程。如果置换率太高，则会出现周期振荡和混沌，系统可能会崩溃。替代理论可以用来解释物理和人类系统中各种复杂的相互作用和转换。更替动力学为研究Volterra-Lotka的捕食者-猎物关系、人地关系以及农民起义导致的王朝变迁等问题提供了新的视角。
英文摘要：
Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a replacement process, and the logistic substitution suggests non-linear dynamical behaviors such as bifurcation and chaos. Using mathematical transform and numerical computation, we can demonstrate that the 1-dimensional map comes from a 2-dimensional two-group interaction map. By analogy with urbanization, a general theory of replacement dynamics is presented in this paper, and the replacement process can be simulated with the 2-dimansional map. If the rate of replacement is too high, periodic oscillations and chaos will arise, and the system maybe breaks down. The replacement theory can be used to interpret various complex interaction and conversion in physical and human systems. The replacement dynamics provides a new way of looking at Volterra-Lotka's predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and so on.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
