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On Boolean Automata Isolated Cycles and Tangential Double-Cycles Dynamics

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Automata and Complexity

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 42))

Abstract

Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical world in which we evolve, is also structured by systems of interacting particles. Interaction networks can be seen in all spheres of existence that concern us, and yet, our understanding of interaction networks remains severely limited by our present lack of both theoretical and applied insight into their clockworks. In the past, efforts at understanding interaction networks have mostly been directed towards applications. This has happened at the expense of developing understanding of the generic and fundamental aspects of interaction networks (properties and behaviours due primarily to the fact that a system is an interaction network, as opposed to properties and behaviours rather due to the fact a system is a genetic interaction network for instance). Intrinsic properties of interaction networks (e.g., the ways in which they transmit information along entities, their ability to produce this or that kind of global dynamical behaviour depending on local interactions) are thus still not well understood. Lack of fundamental knowledge tends to limit the innovating power of applications. Without more theoretical fundamental knowledge, applications cannot evolve deeply and become more impacting. Hence, it is necessary to better apprehend and comprehend the intrinsic properties of interaction networks, notably the relations between their architecture and their dynamics and how they are affected by and set in time. In this chapter, we use the elementary mathematical model of Boolean automata networks as a formal archetype of interaction networks. We survey results concerning the role of feedback cycles and the role of intersections between feedback cycles, in shaping the asymptotic dynamical behaviours of interaction networks. We pay special attention to the impact of the automata updating modes.

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Acknowledgements

This work was funded mainly by our salaries as French or German State agents or pensioner (affiliated to Université Grenoble-Alpes (JD), Université d’Évry (TM and DR), Freie Universität Berlin (MN), and Université d’Aix-Marseille (SS)), and secondarily by the ANR-18-CE40-0002 FANs project (SS).

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Authors and Affiliations

  1. Université publique, Grenoble, France

    Jacques Demongeot

  2. Université publique, Évry, France

    Tarek Melliti & Damien Regnault

  3. Freie Universität Berlin, Berlin, Germany

    Mathilde Noual

  4. Université publique, Marseille, France

    Sylvain Sené

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  1. Jacques Demongeot
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  5. Sylvain Sené
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Correspondence to Sylvain Sené .

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  1. Unconventional Computing Centre, University of the West of England, Bristol, UK

    Andrew Adamatzky

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Demongeot, J., Melliti, T., Noual, M., Regnault, D., Sené, S. (2022). On Boolean Automata Isolated Cycles and Tangential Double-Cycles Dynamics. In: Adamatzky, A. (eds) Automata and Complexity. Emergence, Complexity and Computation, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-030-92551-2_11

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  • DOI: https://doi.org/10.1007/978-3-030-92551-2_11

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