THE APPLICABILITY OF GM(1,N)MODEL TO BIOLOGICAL SYSTEMS
GM(1,N)模型对生物系统应用的研究

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.