Hierarchical evolutive systems: A mathematical model for complex systems
type: Item
instance of: scholarly article
title: Hierarchical evolutive systems: A mathematical model for complex systems
zbMATH Open document ID: 0619.92001
DOI: 10.1007/BF02459958
author: Jean-Paul Vanbremeersch
author: Andrée C. Ehresmann
published in: Bulletin of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: In this paper the notion of an evolutive hierarchical system as a mathematical model for complex systems, such as bio-sociological systems, is proposed. This model is based on category theory and presents the structure of the system as it is defined by its internal organization of any level: its components, their interrelations, their degree of complexity, their changing in time. Functional consequences are drawn from the synchronical and diachronical interactions of the components, and from the fact that the behaviour of a complex component will be determined by that of its own components and their links. The state of the system at a given instant is modeled by a category whose objects are its components, the state transition by a functor, a complex object by the limit of a pattern of linked objects, which describe its internal organization. The properties of limits in a category make it possible to ''measure'' the emergence of properties for a complex object with respect to its components, and to reduce the study of a hierarchical system to that of its components of the lowest degree and their links. Categorical constructions describe the formation of a hierarchical evolutive system stepwise, by means of the operations: absorption of external objects, destruction of some components, formation of new complex objects. So this theory combines the structural, relational and functional approaches and it can be used as a means of obtaining a better evaluation of the characteristic relations of the degree of complexity at each level in the hierarchy of the system. The paper contains a number of natural examples which illustrate the general constructions and main principles of the theory.
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 93A13
Mathematics Subject Classification ID: 93A10
Mathematics Subject Classification ID: 93A15
Mathematics Subject Classification ID: 93A99
Mathematics Subject Classification ID: 93C30
Mathematics Subject Classification ID: 18B99
zbMATH DE Number: 4006039
zbMATH Keywords: evolutive hierarchical system
zbMATH Keywords: complex systems
zbMATH Keywords: category theory
zbMATH Keywords: properties of limits
zbMATH Keywords: absorption of external objects
zbMATH Keywords: destruction
zbMATH Keywords: formation of new complex objects
zbMATH Keywords: degree of complexity
zbMATH Keywords: examples
MaRDI profile type: Publication
Wikidata QID: Q69118174
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description: scientific article; zbMATH DE number 4006039