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On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations

  • Conference paper
Numerical Methods in the Study of Critical Phenomena

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 9))

Summary

Simple feedback loops behave in two essentially different ways depending on whether they contain an odd number of inhibitory elements (“negative” loops) or an even number of inhibitory elements (“positive” loops); for proper values of parameters or delays, the former generate sustained oscillations, the latter, multiple steady states. For more complex systems, as far as one can tell, the presence of at least one negative loop in the logical structure appears as a necessary (but not sufficient) condition for a permanent periodic behaviour, and the presence of at least one positive loop as a necessary (but not sufficient) condition for multiple steady states.

The second part of this paper deals with the cooperative use of Boolean and continuous methods in the field and with the relations between Boolean and quantitative iteration methods.

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Authors and Affiliations

  1. Laboratoire de Génétique, Université Libre de Bruxelles, 67, Rue des Chevaux, 1640, Rhode Saint Genèse, Belgium

    R. Thomas

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  1. R. Thomas
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Editors and Affiliations

  1. Laboratoire d’Informatique et de Mathématiques Appliquées de Grenoble, Université Scientifique et Médicale de Grenoble, F-BP 53X, 38041, Grenoble Cédex, France

    Jean Della Dora , Jacques Demongeot  & Bernard Lacolle ,  & 

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© 1981 Springer-Verlag Berlin Heidelberg

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Thomas, R. (1981). On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations. In: Della Dora, J., Demongeot, J., Lacolle, B. (eds) Numerical Methods in the Study of Critical Phenomena. Springer Series in Synergetics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81703-8_24

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  • DOI: https://doi.org/10.1007/978-3-642-81703-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81705-2

  • Online ISBN: 978-3-642-81703-8

  • eBook Packages: Springer Book Archive

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