MODELS (Use of Generic and Concrete)

Charles François (2004). MODELS (Use of Generic and Concrete), International Encyclopedia of Systems and Cybernetics, 2(2): 2183.

Collection	International Encyclopedia of Systems and Cybernetics
Year	2004
Vol. (num.)	2(2)
ID	◀ 2183 ▶
Object type	Methodology or model

J. ARACIL explains as follows the use of generic and concrete models for the study of nonlinear dynamical systems:

“Once a generic model M has been adopted, we have to choose the model M that ”best“ fits the concrete system. The fitting criterion between and is established from observations of the time behavior of . The model (p)M whose trajectories best fit the ones observed on will be adopted. This fitting criterion can be quantitative, formalized through a mathematical expresion of the discrepancies between the data observed on and the ones generated by . It is very common to use the quadratic value of this discrepancy. This criterion has a strongly local character as far as it refers to a trajectory (the measured one) which is adopted as representative of the behavior mode. However, it is well known that a nonlinear dynamical system'' can have many attractors'' and therefore, can show different behaviors'' associated to them. In that case, if one adopts a single trajectory as representative of the behavior of the system, then one is self-restricted to one attractor, forgetting the other ones, and the analysis of the system is unfailingly defective” (1986, p.245).

This is a characteristical problem presented by FORRESTER's systems dynamics: what happens when some systemic process escapes from its supposedly normal range of trajectories? and what should be done in such case?

ARACIL's qualitative analysis of models tries to solve this problem.