摘要
灰色系统理论的GM(1,N)模型已被广泛地用于生态,农业、林业等与生命现象有关的系统的分析和处理。但GM(1,N)本质上是一线性系统,在生态系统中,由于个体和种群的发展均受个体和种群间对有限资源竞争的限制,一般地说线性假设不能成立。本文对GM(1,N)在生态系统的适应性进行了探讨,提出了系统线性度,系统非线性显著度的概念、定义和具体计算方法,并在此基础上建立了GM(1,N)模型的适用标准。将这一标准施用于计算机模拟的非线性程度不同的生态系统,结果说明本文所提出的系统表征的度量标准基本准确。另外,本文对GM(1,N)中的参数拟合略有改进,新方法在计算上有合理、省时等特点。
GM(1,N) model of the Gray System Theory has been extensively app-lied to the analyses of systems of agriculture, forestry, ecology and manyother life-related systems. The model is mathematically a linear systemmodel with constants coefficients. However the development of both indi-viduals and the population in biological systems is always, to differentextent, affected or limited by finite resources and the competition amongindividuals and populations, which is known to be a primary contributorto the system nonlinearity. Hence the assumption of linearity behind GM(1,N) Model in general is not justified except some special cases. Eventhough the residual model of Gray Theory can be used to improve theaccuracy of the system prediction, it contributes very little to the primarypurpose of system modelling, i,e., to gain insight into the system and tocapture the essence of system mechanism behind the observed data, beca-use the residual model is usually difficult to interpret. This research is astudy on the applicabil ityof GM(1,N) model on biological systems. Twodifferent measurements of system behavior regarding the linearity, thesystem linearity (SL) and the significance of system nonlinearity (SSN)are defined to provide criteria and justification for the application of GM(1,N) model based on the system observations before final model solutionis attempted. When the system does not satisfy the linearity criterion, itis better to seek alternative nonlinear models instead of relying on the re-sidual model, Hence this paper is the also a early step to handle system nonlinearity regarding the Gray Model applications, The developed systembehavior measurements were applied to computer-simulated systems ofdifferent nonlinearity, with results showing consistent measurements. In addition, a different formulation compared to the original GM(1,N) Model is used to obtain the model constants with more precise pre-dictions and, in some cases, less amount of computation.
基金
中国科学院植被数量生态开放实验窒支技的项目"植彼数量分析与不确定建模研究"之一部分。
关键词
灰色系统
模型
生态系统
Gray Theory
Model
Biology
System
Ecology
Nonlinearity
