publication . Preprint . 2010

Nonlinear threshold Boolean automata networks and phase transitions

Demongeot, Jacques; Sené, Sylvain;
Open Access English
  • Published: 21 Nov 2010
  • Publisher: HAL CCSD
  • Country: France
Abstract
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.
Subjects
free text keywords: [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Computer Science - Discrete Mathematics, Mathematics - Dynamical Systems, Nonlinear Sciences - Cellular Automata and Lattice Gases

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