微分方程系统的聚合在生态系统中的应用

介绍了缩减基于微分方程系统规模和复杂度的一种方法——聚合。系统的微分方程包括:快速部分和慢速部分。假设快速部分是守恒的,则选择宏观层上相对快速部分不发生变化的量为聚合变量,运用快速推导法来缩减微观模型,并且介绍了此方法在生态系统中的应用实例。同时阐述了聚合模型表现出与原模型不同的行为特性,称为行为突现。

Application of Aggregation of Differential Equation Systems to Ecology Systems

The aim of this article is to present a method to reduce the dimension and complexity of differential equation system, i.e, aggregation. The differential equation of the system is composed of fast parts and slow parts. The fast dynamics are assumed to be conservative. The invariables coprresponding to the fast parts in the macro-level are choosen as aggregation variables, and the quick derivation method is used to reduce the initial model. The practical examples of applying this method to ecological system is introduced. It is also elaborated that the aggregation model presents new behavior characteristics different from other models, i.e, sudden behavior emergence.