Publication details for Dr Maximilien GadouleauGadouleau, Maximilien & Richard, Adrien (2016). Simple dynamics on graphs. Theoretical Computer Science 628: 62-77.
- Publication type: Journal Article
- ISSN/ISBN: 0304-3975
- DOI: 10.1016/j.tcs.2016.03.013
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
Can the interaction graph of a finite dynamical system force this system to have a “complex” dynamics? In other words, given a finite interval of integers A, which are the signed digraphs G such that every finite dynamical system f:An→An with G as interaction graph has a “complex” dynamics? If |A|≥3 we prove that no such signed digraph exists. More precisely, we prove that for every signed digraph G there exists a system f:An→An with G as interaction graph that converges toward a unique fixed point in at most ⌊log2n⌋+2 steps. The boolean case |A|=2 is more difficult, and we provide partial answers instead. We exhibit large classes of unsigned digraphs which admit boolean dynamical systems which converge toward a unique fixed point in polynomial, linear or constant time.