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.