Negative circuits and sustained oscillations in asynchronous automata networks

Details Negative circuits and sustained oscillations in asynchronous automata networks Negative circuits and sustained oscillations in asynchronous automata networks

2009-07-29

arxiv.org/abs/0907.5096v1

Computer Science

Discrete Mathematics

Scientific paper

The biologist Ren\'e 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 for this system to produce sustained oscillations. In this paper, we state and prove this conjecture for asynchronous automata networks, a class of discrete dynamical systems extensively used to model the behaviors of gene networks. As a corollary, we obtain the following fixed point theorem: given a product $X$ of $n$ finite intervals of integers, and a map $F$ from $X$ to itself, if the interaction graph associated with $F$ has no negative circuit, then $F$ has at least one fixed point.

Affiliated with

Also associated with

No associations

Rating

Negative circuits and sustained oscillations in asynchronous automata networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Negative circuits and sustained oscillations in asynchronous automata networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Negative circuits and sustained oscillations in asynchronous automata networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-521509