Creation of fixed points in block-parallel Boolean automata networks
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913961737191424 |
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| author | Perrot, Kévin Sené, Sylvain Tapin, Léah |
| author_facet | Perrot, Kévin Sené, Sylvain Tapin, Léah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Creation of fixed points in block-parallel Boolean automata networks Perrot, Kévin Sené, Sylvain Tapin, Léah Discrete Mathematics 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. |
| title | Creation of fixed points in block-parallel Boolean automata networks |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2505.15499 |