Communication Dans Un Congrès Année : 2025

Creation of fixed points in block-parallel Boolean automata networks

Kévin Perrot
Sylvain Sené

Résumé

In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a collection of Boolean entities (the automata) update their state depending on the states of others. Fixed points represent phenotypes such as differentiated cell types. The interaction graph of a BAN captures the architecture of dependencies among its automata. A first seminal result is that cycles of interactions (so called feedbacks) are the engines of dynamical complexity. A second seminal result is that fixed points are invariant under block-sequential update schedules, which update the automata following an ordered partition of the set of automata. In this article we study the ability of block-parallel update schedules (dual to the latter) to break this fixed point invariance property, with a focus on the simplest feedback mechanism: the canonical positive cycle. We quantify numerically the creation of new fixed points, and provide families of block-parallel update schedules generating exponentially many fixed points on this elementary structure of interaction.

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hal-05149054 , version 1 (07-07-2025)

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Kévin Perrot, Sylvain Sené, Léah Tapin. Creation of fixed points in block-parallel Boolean automata networks. International Conference on Unconventional Computation and Natural Computation, Sep 2025, Nice, France. ⟨hal-05149054⟩
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