VARIATIONAL PRINCIPLES AND CONSERVATION CONDITIONS IN VOLTERRA'S ECOLOGY AND IN URBAN RELATIVE DYNAMICS*
在沃尔泰拉-洛特卡模型下分析相对空间人口动力学，推导出变分原理，发现其积分平稳值对应人口分布的时间累积熵，并与经济理论中的优化原理进行解释。
ABSTRACT. Relative spatial population dynamics are analyzed in this paper under Volterra‐Lotka specifications. At first, the Volterra conservation conditions under absolute growth and their variational principles are reviewed, extended, and interpreted. Then, the relative dynamics are presented which demonstrate the presence of competitive exclusion. The main aim is to derive the variational principles underlying relative population dynamics. It is found that these principles produce an integrand, the stationary value of its integral being the cumulative entropy of the population distribution over a time horizon. Substantive interpretation of these results in accordance with optimization principles in economic theory is presented.