Journal of Mathematical Biology

, Volume 63, Issue 3, pp 593–600 | Cite as

Stable periodicity and negative circuits in differential systems

Article

Abstract

We provide a counter-example to a conjecture of René Thomas on the relationship between negative feedback circuits and stable periodicity in ordinary differential equation systems (Kaufman et al. in J Theor Biol 248:675–685, 2007). We also prove a weak version of this conjecture by using a theorem of Snoussi.

Keywords

Feedback circuit Regulatory network Oscillation Jacobian matrix Interaction graph 

Mathematics Subject Classification (2000)

34C10 92C42 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.I3S, UMR 6070 CNRS, Université de Nice-Sophia AntipolisSophia AntipolisFrance

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