Abstract
The arithmetical relator is a new mathematical tool for the modelization of natural systems, mainly physical and biological ones. Essentially, it expresses the adaptation of a system to its environment and may take into account many imbrication levels. Several examples, especially in biology, has been obtained by a holistic approach, at different organization levels. But in order to prove the physical relevance of these models and to increase the easiness for finding them, a new presentation of this tool and an attempt of connection with the integro-differential formalism have been developed. We use a “building of neighbourhoods” applied to different complementary kinds of models : degenerated, linearized, multiquadratic. This “building” combines the underlying dynamics, the positioning of the reference frames and the class of processing in a multi-levelled system. A very simple example illustrates the “opening-closing” dynamics. Some results in physics are briefly presented.
Work sponsored by Direction des Recherches, Etudes et Techniques (Delegation Générale pour l’Armement, Ministère de la Défense, Paris).
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Moulin, T.M., Vallet, C.M. (1988). Application of a “Building of Neighbourhoods” to the Modelization of Natural Systems. In: Carvallo, M.E. (eds) Nature, Cognition and System I. Theory and Decision Library, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2991-3_13
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DOI: https://doi.org/10.1007/978-94-009-2991-3_13
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