Stable periodicity and negative circuits in differential systems.
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.
I3S, UMR 6070 CNRS, Université de Nice-Sophia Antipolis, 2000 route des Lucioles, 06903 Sophia Antipolis, France. richard@unice.fr
Adrien
A
Richard
Jean-Paul
JP
Comet
D005246:Feedback; D008954:Models, Biological; D010507:Periodicity