A necessary condition for boundary sensitivity of attractive non-linear stochastic cellular automata in ZxZ

Sylvain Sené (1, 2)

1 IXXI - Institut Rhône-Alpin des systèmes complexes
2 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes

This paper tackles the question of the environmental robustness of a particular class of two-dimensional finite threshold Boolean cellular automata when they are subjected to distinct fixed boundary instances. More precisely, focusing on a non-linear stochastic version of the classical threshold function governing the evolution of formal neural networks, we show the existence of a necessary condition under which attractive cellular automata of this form become boundary sensitive, i.e., we highlight a condition without which a cellular automaton hits the same asymptotic dynamical behaviour whatever its boundary conditions are. To go further, we give an explicit formula for this necessary condition.

Mots clés: Boolean automata networks; synchronism sensitivity; XOR circulant networks; convergence time

Domaines: Mathématique discrète [cs.DM]

Sylvain Sené. A necessary condition for boundary sensitivity of attractive non-linear stochastic cellular automata in ZxZ. 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires (AUTOMATA&JAC 2012), Sep 2012, La Marana, France. pp.1--10. ⟨hal-00783508⟩