2010/11/21 by Jacques Demongeot, Demongeot, Jacques, Sylvain Sené +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Markov Chains and Monte Carlo Methods #cs.DM #math.DS #nlin.CG
paper · pdf · doi:10.48550/arxiv.1011.4675
arxiv created 2010/11/21 · openalex publication_date 2010/11/21 · arxiv updated 2010/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.