Nonlinear threshold Boolean automata networks and phase transitions

TL;DR

This paper introduces a formal framework for analyzing phase transitions in nonlinear stochastic threshold Boolean automata networks, highlighting how local interactions influence global emergent behaviors.

Contribution

It develops a novel formal approach to characterize phase transitions in nonlinear Boolean automata networks considering local interaction potentials.

Findings

Derived conditions for phase transitions in nonlinear networks

Identified how local interaction potentials affect global dynamics

Extended classical models to include nonlinear terms

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.