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.
KeywordsFeedback circuit Regulatory network Oscillation Jacobian matrix Interaction graph
Mathematics Subject Classification (2000)34C10 92C42
Unable to display preview. Download preview PDF.
- Perko L (2002) Differential equations and dynamical systems. Springer, BerlinGoogle Scholar
- Thomas R (1981) On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. Synergetics, vol 9, pp 180–193. Springer, BerlinGoogle Scholar