Nonlinear threshold Boolean automata networks and phase transitions

Jacques Demongeot (1) , Sylvain Sené (2, 3)

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

In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on the basis of classical stochastic threshold Boolean automata networks in which specific interaction potentials of neighbourhood coalition are taken into account. More precisely, specific nonlinear terms compose local transition functions that define locally the dynamics of such networks. Basing our study on nonlinear networks, we exhibit new results, from which we derive conditions of phase transitions.

Domaines: Mathématique discrète [cs.DM]; Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Jacques Demongeot, Sylvain Sené. Nonlinear threshold Boolean automata networks and phase transitions. 2010. ⟨hal-00538953⟩