突变模型势函数的一般表示式及用于富营养化评价

通常的初等突变评价模型仅给出控制变量维数n≤4的突变模型的势函数及相应的归一化公式,对高维(n≥5)的复杂系统需将其分解为若干维数小于4的多层子系统后再递归进行,且一般只给出各评价结果的相对排序.通过对初等突变模型势函数形式和相应的归一化公式的观察、比较和分析归纳,推演出包括任意维的突变模型的势函数形式及其相应的归一化公式.将推导出的突变评价归一化公式和分层递阶降维突变评价模型相结合,实现对指标众多的复杂系统的评价和分类.将突变评价公式应用于北京市21个湖泊的富营养化评价,并与多种评价方法进行了比较.结果表明,除1个湖泊的评价结果有相邻一级之差外,其余20个湖泊的评价结果完全一致,表明推演出的高维突变势函数形式和归一化公式是合理的.将其用于湖泊富营养化评价具有简单、实用的特点.

Generalized expression of potential function in catastrophe model and its application in eutrophication evaluation

Usually, elementary catastrophe models can only result in potential function forms and the corresponding normalization formulae with control variable dimensions n ≤ 4. While for the complex system of n ≥ 5, the system has to be first decomposed into several multi-layer subsystems of n ≤ 4, and then the recursive approach is used to resolve the subsystems.The evaluation results of the complex system are generally given in the context of relative ordering.A generalized expression of potential function in catastrophe model and the corresponding normalization formula with unlimited dimensions for control variables are arrived through observation, comparison, analysis, and induction of the results of elementary catastrophe models.The complex systems with multi-indexes (control variables) can be evaluated and classified using the combined approach of the corresponding normalization formula resulted from the generalized expression and the hierarchical dimension reduction technique.The combined approach is applied to evaluate eutrophication in 21 Beijing lakes.The results are compared with the several reports on the same subject and for the same lakes, showing that 20 out of 21 eutrophication evaluations are consistent with other studies and our generalized expression of potential function and the corresponding normalization formula are reasonable and simple, practical to apply in the eutrophication evaluation.