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Durham University

Computer Science


Publication details for Dr Maximilien Gadouleau

Gadouleau, Maximilien & Richard, Adrien (2016). Simple dynamics on graphs. Theoretical Computer Science 628: 62-77.

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 ⌊log2⁡n⌋+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.