2 papers
cs.DM2009★ 1 cited
Negative circuits and sustained oscillations in asynchronous automata networks
Adrien Richard
The biologist René Thomas conjectured, twenty years ago, that the presence of a negative feedback circuit in the interaction graph of a dynamical system is a necessary condition fo…
cs.DM2008
Positive circuits and maximal number of fixed points in discrete dynamical systems
Adrien Richard
We consider the Cartesian product X of n finite intervals of integers and a map F from X to itself. As main result, we establish an upper bound on the number of fixed points for F…