1 citations · 1 across the 4 of their papers we have counts for
4 papers
Local negative circuits and fixed points in Boolean networks
Adrien Richard
To each Boolean function F from {0,1}^n to itself and each point x in {0,1}^n, we associate the signed directed graph G_F(x) of order n that contains a positive (resp. negative) ar…
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…
On the length of attractors in boolean networks with an interaction graph by layers
Adrien Richard
We consider a boolean network whose interaction graph has no circuit of length >1. Under this hypothesis, we establish an upper bound on the length of the attractors of the network…
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…