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The emergence of dynamic networks from many coupled polar oscillators: a paradigm for artificial life

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Abstract

This work concerns a many-body deterministic model that displays life-like properties such as emergence, complexity, self-organization, self-regulation, excitability and spontaneous compartmentalization. The model portraits the dynamics of an ensemble of locally coupled polar phase oscillators, moving in a two-dimensional space, that under certain conditions exhibit emergent superstructures. Those superstructures are self-organized dynamic networks, resulting from a synchronization process of many units, over length scales much greater than the interaction range. Such networks compartmentalize the two-dimensional space with no a priori constraints, due to the formation of porous transport walls, and represent a highly complex and novel non-linear behavior. The analysis is numerically carried out as a function of a control parameter showing distinct regimes: static pattern formation, dynamic excitable networks formation, intermittency and chaos. A statistical analysis is drawn to determine the control parameter ranges for the various behaviors to appear. The model and the results shown in this work are expected to contribute to the field of artificial life.

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All relevant data are within the paper and its Supporting Information files.

References

  • Acebrón JA, Bonilla LL, Vicente P, Conrad J, Ritort F, Spigler R (2005) The Kuramoto model: a simple paradigm for synchronization phenomena. Rev Mod Phys 77(1):137–185

    Article  Google Scholar 

  • Adami C (1998) Introduction to artificial life. Springer, Berlin

    Book  Google Scholar 

  • Baeck T, Fogel D, Michalewicz Z (1997) Handbook of evolutionary computation. Taylor & Francis, London

    Book  Google Scholar 

  • Bar-Yam Y (1997) Dynamics of complex systems (studies in nonlinearity). Westview Press, Boulder, CO

    Google Scholar 

  • Bedau MA (2003) Artificial life: organization, adaptation and complexity from the bottom up. Trends Cogn Sci (Regul Ed) 7: 505–512

  • Bedau MA (2007) “Artificial life”. In: Gabbay DM, Thagard P, Woods J (eds) Handbook of the philosophy of science. Matthen M, Stephens C (eds) Philosophy of biology, vol 3. Elsevier BV, Amsterdam, pp 585–603

  • Benner SA, Sismour AM (2005) Synthetic biology. Nat Rev Genet 6:533–543

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Boden M (1996) The philosophy of artificial life (Oxford readings in philosophy series). Oxford University Press, Oxford

    Google Scholar 

  • Breakspear M, Heitmann S, Daffertshofer A (2010) Generative models of cortical oscillations: neurobiological implications of the Kuramoto model. Front Hum Neurosci 4(190):190

    PubMed  PubMed Central  Google Scholar 

  • Cangelosi A, Parisi D (2002) Simulating the evolution of language. Springer, London

    Book  Google Scholar 

  • Christiansen M, Kirby S (2003) Language evolution. Oxford University Press, Oxford

    Book  Google Scholar 

  • Clark A (1997) Being there: putting brain, body, and world together again. MIT Press, Cambridge, MA

    Google Scholar 

  • Coello CAC, Lamont GB, Van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems (genetic and evolutionary computation), 2nd edn. Springer, New York

    Google Scholar 

  • Couzin ID (2009) Collective cognition in animal groups. Trends Cogn Sci (Regul Ed) 13: 36–43

  • Cross MC, Hohenberg PC (1993) Pattern formation outside of equilibrium. Rev Mod Phys 65:851

    Article  CAS  Google Scholar 

  • De Castro L (2006) Fundamentals of natural computing: basic concepts, algorithms, and applications. Chapman & Hall/CRC Computer & Information Science Series, Taylor & Francis, Florida

  • Dorin A (2014) Biological bits: a brief guide to the ideas and artefacts of computational artificial life. Animaland, Melbourne

  • Ermentrout B (1991) An adaptive model for synchrony in the firefly Pteroptyx malaccae. J Math Biol 29:571–585

    Article  Google Scholar 

  • Klinshov V, Franović I (2019) Two scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators. Phys Rev E 100:062211

    Article  PubMed  Google Scholar 

  • Krolikowski R, Kopys M, Jedruch W et al (2016) Self-organization in multi-agent systems based on examples of modeling economic relationships between agents. Computational Intelligence in Robotics, vol 3

  • Kuramoto Y (1975) Lecture notes in physics. In: Araki H (ed) International symposium on mathematical problems in theoretical physics, vol 39. Springer-Verlag, New York, pp 420–430

  • Lafuerza LF, Colet P, Toral R (2010) Nonuniversal results induced by diversity distribution in coupled excitable systems. Phys Rev Lett 105:084101

    Article  PubMed  Google Scholar 

  • Langton CG (1997) Artificial life: an overview. MIT Press, Cambridge, MA

    Google Scholar 

  • Langton CG (ed) (1989) Artificial life: proceedings of an interdisciplinary workshop on the synthesis and simulation of living systems. Addison-Wesley, Los Alamos. Complex adaptive systems

  • Luisi P (2006) The emergence of life. From chemical origins to synthetic biology. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Luisi P (2014) Prebiotic metabolic networks? Mol Syst Biol 10(4): 729

  • Maes P (1993) Modeling adaptive autonomous agents. Art Life 1:135–162

    Article  Google Scholar 

  • Matarić M, Cliff D (1996) Challenges in evolving controllers for physical robots. Rob Auton Syst 19:67–83

    Article  Google Scholar 

  • Maynard Smith J, Szathmáry E (1995) The major transitions in evolution. Oxford University Press, New York

    Google Scholar 

  • Mitchell M (2009) Complexity: a guided tour. Oxford University Press, Oxford

    Google Scholar 

  • Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256

    Article  Google Scholar 

  • Newman M, Barabási AL, Watts DJ (eds) (2006) The structure and dynamics of networks (Princeton studies in complexity). Princeton University Press, Princeton, NJ

    Google Scholar 

  • Osaka M (2017) Modified Kuramoto phase model for simulating cardiac pacemaker cell synchronization. Appl Math 8(9): 1227–1238

  • Rasmussen S, Chen L, Nilsson M, Abe S (2003) Bridging nonliving and living matter. Artif Life 9:269–316

    Article  PubMed  Google Scholar 

  • Rasmussen S, Bedau M, Hen L, Deamer D, Krakauer DC, Packard NH (eds) (2008) Protocells: bridging nonliving and living matter. MIT Press, Cambridge, MA

    Google Scholar 

  • Rodrigues FA, Peron TK, Ji P, Kurths J (2016) The Kuramoto model in complex networks. Phys Rep 610:1–98

    Article  Google Scholar 

  • Scirè A, Annovazzi-Lodi V (2017) Self-organization in a diversity induced thermodynamics. PLoS ONE 12(12): e0188753

  • Sigmund K (1993) Games of life: explorations in ecology, evolution and behaviour. Oxford University Press Inc, New York, NY

    Google Scholar 

  • Steels L, Brooks R (1995) The artificial life route to artificial intelligence: building embodied, situated agents. L. Erlbaum Associates, Hillsdale, NJ

  • Tessone CJ, Scirè A, Toral R, Colet P (2007) Theory of collective firing induced by noise or diversity in excitable media. Phys Rev E Stat Nonlin Soft Matter Phys 75(1 Pt 2): 016203

  • Waddington C (ed) (1968) Biological processes in living systems: toward a theoretical biology. Aldine Transaction, Chicago, IL

    Google Scholar 

  • Webb B (2000) What does robotics offer animal behaviour? Anim Behav 60:545–558

    Article  CAS  PubMed  Google Scholar 

  • Winfree AT (1990) The geometry of biological time. (Springer study edition). Springer-Verlag

  • Wolfram S (2002) A new kind of science. Wolfram Media, New York, NY

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Acknowledgements

A.S. Acknowledges Giuseppe Aromataris (University of Pavia, Pavia, Italy) and Emilio Hernandez-Garcia (Instituto de Fisica Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain) for fruitful conversations.

Funding

The authors received no specific funding for this work.

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Authors and Affiliations

  1. Dipartimento Di Ingegneria Industriale E Dell’Informazione, Università Di Pavia, 27100, Pavia, Italy

    Alessandro Scirè & Valerio Annovazzi-Lodi

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  1. Alessandro Scirè
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  2. Valerio Annovazzi-Lodi
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Contributions

A.S. performed the numerical simulations, wrote the main manuscript text, prepared the figures and the supporting information files. V. A. L. discussed the general organization and focus of the research. All authors reviewed the manuscript.

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Correspondence to Alessandro Scirè.

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Supplementary Information

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Supplementary file1 (MP4 18255 kb) Spatio-temporal dynamics resulting from a numerical simulation of Eqs. (1)-(2). N = 500 (250 c-poles and 250 s-poles). Detuning parameter ΔH =0.

Supplementary file2 (MP4 97054 kb) Spatio-temporal dynamics resulting from a numerical simulation of Eqs. (1)-(2). N = 500 (250 c-poles and 250 s-poles). Detuning parameter ΔH =0.1. A time counter has been added to the movie in order to better connect the spatio-temporal dynamics to Fig.5.

Supplementary file3 (MP4 389225 kb) Spatio-temporal dynamics resulting from a numerical simulation of Eqs. (1)-(2). N = 400 (200 c-poles and 200 s-poles). Detuning parameter ΔH =0.15.

Supplementary file4 (MP4 74740 kb) Spatio-temporal dynamics resulting from a numerical simulation of Eqs. (1)-(2). N = 500 (250 c-poles and 250 s-poles). Detuning parameter ΔH =0.2.

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Scirè, A., Annovazzi-Lodi, V. The emergence of dynamic networks from many coupled polar oscillators: a paradigm for artificial life. Theory Biosci. 142, 291–299 (2023). https://doi.org/10.1007/s12064-023-00401-4

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