IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v7y2016i3p24-d77758.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/7/3/24/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/7/3/24/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Felix J H Hol & Peter Galajda & Krisztina Nagy & Rutger G Woolthuis & Cees Dekker & Juan E Keymer, 2013. "Spatial Structure Facilitates Cooperation in a Social Dilemma: Empirical Evidence from a Bacterial Community," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.
    3. 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).
    4. Tan, Bing Qing & Kang, Kai & Zhong, Ray Y., 2023. "Electric vehicle charging infrastructure investment strategy analysis: State-owned versus private parking lots," Transport Policy, Elsevier, vol. 141(C), pages 54-71.
    5. Brian McLoone & Wai-Tong Louis Fan & Adam Pham & Rory Smead & Laurence Loewe, 2018. "Stochasticity, Selection, and the Evolution of Cooperation in a Two-Level Moran Model of the Snowdrift Game," Complexity, Hindawi, vol. 2018, pages 1-14, February.
    6. Thomas Graham & Maria Kleshnina & Jerzy A. Filar, 2023. "Where Do Mistakes Lead? A Survey of Games with Incompetent Players," Dynamic Games and Applications, Springer, vol. 13(1), pages 231-264, March.
    7. Florian Brandl & Felix Brandt, 2021. "A Natural Adaptive Process for Collective Decision-Making," Papers 2103.14351, arXiv.org, revised Mar 2024.
    8. Xiaodan Kong & Qi Xu & Tao Zhu, 2019. "Dynamic Evolution of Knowledge Sharing Behavior among Enterprises in the Cluster Innovation Network Based on Evolutionary Game Theory," Sustainability, MDPI, vol. 12(1), pages 1-23, December.
    9. Lin, XuXun & Yuan, PengCheng, 2018. "A dynamic parking charge optimal control model under perspective of commuters’ evolutionary game behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1096-1110.
    10. Han, Zhi-Quan & Liu, Tong & Liu, Hua-Feng & Hao, Xiao-Ran & Chen, Wei & Li, Bai-Lian, 2019. "Derivation of species interactions strength in a plant community with game theory," Ecological Modelling, Elsevier, vol. 394(C), pages 27-33.
    11. Jida Liu & Changqi Dong & Shi An & Yanan Guo, 2021. "Research on the Natural Hazard Emergency Cooperation Behavior between Governments and Social Organizations Based on the Hybrid Mechanism of Incentive and Linkage in China," IJERPH, MDPI, vol. 18(24), pages 1-27, December.
    12. Chaitanya Gokhale & Arne Traulsen, 2014. "Evolutionary Multiplayer Games," Dynamic Games and Applications, Springer, vol. 4(4), pages 468-488, December.
    13. Antun Skanata & Edo Kussell, 2021. "Ecological memory preserves phage resistance mechanisms in bacteria," Nature Communications, Nature, vol. 12(1), pages 1-12, December.
    14. Pigolotti, S. & Benzi, R. & Perlekar, P. & Jensen, M.H. & Toschi, F. & Nelson, D.R., 2013. "Growth, competition and cooperation in spatial population genetics," Theoretical Population Biology, Elsevier, vol. 84(C), pages 72-86.
    15. Marco Alberto Javarone, 2016. "Modeling Poker Challenges by Evolutionary Game Theory," Games, MDPI, vol. 7(4), pages 1-10, December.
    16. Wang, Yijia & Chen, Xiaojie & Wang, Zhijian, 2017. "Testability of evolutionary game dynamics based on experimental economics data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 455-464.
    17. Zhang, Yao & Hao, Qing-Yi & Qian, Jia-Li & Wu, Chao-Yun & Guo, Ning & Ling, Xiang, 2024. "The cooperative evolution in the spatial prisoner's dilemma game with the local loyalty of two-strategy," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    18. Asher Leeks & Stuart A. West & Melanie Ghoul, 2021. "The evolution of cheating in viruses," Nature Communications, Nature, vol. 12(1), pages 1-14, December.
    19. Zhang, Hao & Wang, Mingyue & Cheng, Zhixuan & Wan, Ling, 2020. "Technology-sharing strategy and incentive mechanism for R&D teams of manufacturing enterprises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    20. Xu, Bin & Zhou, Hai-Jun & Wang, Zhijian, 2013. "Cycle frequency in standard Rock–Paper–Scissors games: Evidence from experimental economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4997-5005.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:7:y:2016:i:3:p:24-:d:77758. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.