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On co-evolution and the importance of initial conditions

Author

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  • Lambiotte, Renaud
  • González-Avella, Juan Carlos

Abstract

We present a generic threshold model for the co-evolution of the structure of a network and the binary state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is shown that the system displays a transition from a connected phase to a fragmented phase, and that this transition is driven by the initial configuration of the system, as different initial conditions may lead to drastically different final configurations. Computer simulations are performed and confirm the theoretical predictions.

Suggested Citation

  • Lambiotte, Renaud & González-Avella, Juan Carlos, 2011. "On co-evolution and the importance of initial conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 392-397.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:2:p:392-397
    DOI: 10.1016/j.physa.2010.09.024
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    Cited by:

    1. Toruniewska, Joanna & Suchecki, Krzysztof & Hołyst, Janusz A., 2016. "Unstable network fragmentation in co-evolution of Potts spins and system topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 1-15.
    2. Stefani, Silvana & Ausloos, Marcel & González-Concepción, Concepción & Sonubi, Adeyemi & Gil-Fariña, Ma Candelaria & Pestano-Gabino, Celina & Moretto, Enrico, 2021. "Competing or collaborating, with no symmetrical behaviour: Leadership opportunities and winning strategies under stability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 489-504.

    More about this item

    Keywords

    Co-evolution; Complex networks;

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