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The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games

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  • Mauro Mobilia

    (Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

  • Alastair M. Rucklidge

    (Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

  • Bartosz Szczesny

    (Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

Abstract

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system’s deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed.

Suggested Citation

  • Mauro Mobilia & Alastair M. Rucklidge & Bartosz Szczesny, 2016. "The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games," Games, MDPI, vol. 7(3), pages 1-12, September.
    • Handle: RePEc:gam:jgames:v:7:y:2016:i:3:p:24-:d:77758
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    References listed on IDEAS

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    1. Q. He & M. Mobilia & U. Täuber, 2011. "Coexistence in the two-dimensional May-Leonard model with random rates," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 82(1), pages 97-105, July.
    2. Benjamin Kerr & Claudia Neuhauser & Brendan J. M. Bohannan & Antony M. Dean, 2006. "Local migration promotes competitive restraint in a host–pathogen 'tragedy of the commons'," Nature, Nature, vol. 442(7098), pages 75-78, July.
    3. Frey, Erwin, 2010. "Evolutionary game theory: Theoretical concepts and applications to microbial communities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4265-4298.
    4. Q. He & U. Täuber & R. Zia, 2012. "On the relationship between cyclic and hierarchical three-species predator-prey systems and the two-species Lotka-Volterra model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(4), pages 1-13, April.
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    Cited by:

    1. Park, Junpyo, 2018. "Multistability of extinction states in the toy model for three species," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 92-98.
    2. Yang, Ryoo Kyung & Park, Junpyo, 2023. "Evolutionary dynamics in the cyclic competition system of seven species: Common cascading dynamics in biodiversity," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Bazeia, D. & de Oliveira, B.F. & Silva, J.V.O. & Szolnoki, A., 2020. "Breaking unidirectional invasions jeopardizes biodiversity in spatial May-Leonard systems," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    4. Bazeia, D. & Bongestab, M. & de Oliveira, B.F. & Szolnoki, A., 2021. "Effects of a pestilent species on the stability of cyclically dominant species," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. Szolnoki, Attila & Chen, Xiaojie, 2020. "Strategy dependent learning activity in cyclic dominant systems," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    6. Tian-Jiao Feng & Jie Mei & Rui-Wu Wang & Sabin Lessard & Yi Tao & Xiu-Deng Zheng, 2022. "Noise-Induced Quasi-Heteroclinic Cycle in a Rock–Paper–Scissors Game with Random Payoffs," Dynamic Games and Applications, Springer, vol. 12(4), pages 1280-1292, December.
    7. Park, Junpyo & Chen, Xiaojie & Szolnoki, Attila, 2023. "Competition of alliances in a cyclically dominant eight-species population," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    8. Park, Junpyo, 2021. "Evolutionary dynamics in the rock-paper-scissors system by changing community paradigm with population flow," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Szolnoki, Attila & Perc, Matjaž, 2023. "Oppressed species can form a winning pair in a multi-species ecosystem," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    10. de Oliveira, Breno F. & Szolnoki, Attila, 2022. "Competition among alliances of different sizes," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    11. Huang, Wenting & Duan, Xiaofang & Qin, Lijuan & Park, Junpyo, 2023. "Fitness-based mobility enhances the maintenance of biodiversity in the spatial system of cyclic competition," Applied Mathematics and Computation, Elsevier, vol. 456(C).

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