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

  • R. Thomas
Part of the Springer Series in Synergetics book series (SSSYN, volume 9)


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.


Logical Structure Logical Equation Stable Steady State Future Production Oriented Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • R. Thomas
    • 1
  1. 1.Laboratoire de GénétiqueUniversité Libre de BruxellesRhode Saint GenèseBelgium

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