J. ARACIL seeks a way out of limited quantitative analysis of dynamical nonlinear systems and proposes the following method: "… when a nonlinear dynamical system is analyzed, before adapting a quantitative criterion relative to a behavior mode (attractor) is it convenient to study the full class of behavior modes that the system can show. That is, before trying to make a trajectory generated by µ fit some observations on ´, it should be analyzed if all the behavior modes that can show µ correspond to the ones that show ´. This is the purpose of the qualitative analysis of µ.
"To carry out this analysis we use the phase portrait of µ, in which the attractor's structure of the model µ is shown. Associated with every attractor there is a basin of attraction. The basins are enclosed by separatrixes. The state space is partitioned in the set of basins. The phase portrait supplies an overall view of all the behavior modes the system can show." (1986, p.245)
ARACIL bases his qualitative analysis on THOM's elementary catastrophes, taking in account situations characterized by two alternating attractors. It should be interesting to study what happens when the system undergoes a process of dissipative structuration: this is obviously the case of numerous concrete systems, especially complex ecological, economic, business and social systems.
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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