Stable periodicity and negative circuits in differential systems
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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
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