IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v499y2018icp142-147.html

Dynamic fractals in spatial evolutionary games

Author

Listed:
  • Kolotev, Sergei
  • Malyutin, Aleksandr
  • Burovski, Evgeni
  • Krashakov, Sergei
  • Shchur, Lev

Abstract

We investigate critical properties of a spatial evolutionary game based on the Prisoner’s Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases.

Suggested Citation

  • Kolotev, Sergei & Malyutin, Aleksandr & Burovski, Evgeni & Krashakov, Sergei & Shchur, Lev, 2018. "Dynamic fractals in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 142-147.
    • Handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:142-147
    DOI: 10.1016/j.physa.2018.02.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118300773
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.02.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Adler, Joan, 1991. "Bootstrap percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(3), pages 453-470.
    2. Dirk Helbing, 2013. "Globally networked risks and how to respond," Nature, Nature, vol. 497(7447), pages 51-59, May.
    3. Shiguo Jiang & Desheng Liu, 2012. "Box-Counting Dimension of Fractal Urban Form: Stability Issues and Measurement Design," International Journal of Artificial Life Research (IJALR), IGI Global, vol. 3(3), pages 41-63, July.
    Full references (including those not matched with items on IDEAS)

    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. Balint, T. & Lamperti, F. & Mandel, A. & Napoletano, M. & Roventini, A. & Sapio, A., 2017. "Complexity and the Economics of Climate Change: A Survey and a Look Forward," Ecological Economics, Elsevier, vol. 138(C), pages 252-265.
    2. Weidong Lin & Jose Olmo & Abderrahim Taamouti, 2025. "Portfolio Selection under Systemic Risk," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 57(4), pages 905-949, June.
    3. Sellevåg, Stig Rune, 2021. "Changes in inoperability for interdependent industry sectors in Norway from 2012 to 2017," International Journal of Critical Infrastructure Protection, Elsevier, vol. 32(C).
    4. Igor Linkov & Benjamin Trump & Greg Kiker, 2022. "Diversity and inclusiveness are necessary components of resilient international teams," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 9(1), pages 1-5, December.
    5. Xiao‐Bing Hu & Hang Li & XiaoMei Guo & Pieter H. A. J. M. van Gelder & Peijun Shi, 2019. "Spatial Vulnerability of Network Systems under Spatially Local Hazards," Risk Analysis, John Wiley & Sons, vol. 39(1), pages 162-179, January.
    6. repec:plo:pone00:0090265 is not listed on IDEAS
    7. Man Li & Tao Ye & Peijun Shi & Jian Fang, 2015. "Impacts of the global economic crisis and Tohoku earthquake on Sino–Japan trade: a comparative perspective," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 75(1), pages 541-556, January.
    8. Laura M. Canevari‐Luzardo & Frans Berkhout & Mark Pelling, 2020. "A relational view of climate adaptation in the private sector: How do value chain interactions shape business perceptions of climate risk and adaptive behaviours?," Business Strategy and the Environment, Wiley Blackwell, vol. 29(2), pages 432-444, February.
    9. Gil, Maria Angeles & Gonzalez-Rodriguez, Gil & Colubi, Ana & Montenegro, Manuel, 2007. "Testing linear independence in linear models with interval-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3002-3015, March.
    10. Niccolò Casnici & Pierpaolo Dondio & Roberto Casarin & Flaminio Squazzoni, 2015. "Decrypting Financial Markets through E-Joint Attention Efforts: On-Line Adaptive Networks of Investors in Periods of Market Uncertainty," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-15, August.
    11. Zhao, Yujia & McLellan, Benjamin Craig & Wang, Chaofan & Shuai, Jing & Xiang, Wanting & Shuai, Chuanmin, 2026. "Risk dynamics and strategies of China's solar PV industry chain under trade frictions: A review," Energy Policy, Elsevier, vol. 208(C).
    12. Yoshiharu Maeno & Kenji Nishiguchi & Satoshi Morinaga & Hirokazu Matsushima, 2014. "Impact of credit default swaps on financial contagion," Papers 1411.1356, arXiv.org.
    13. Ellinas, Christos & Allan, Neil & Johansson, Anders, 2016. "Project systemic risk: Application examples of a network model," International Journal of Production Economics, Elsevier, vol. 182(C), pages 50-62.
    14. Franco Bagnoli & Tommaso Matteuzzi, 2025. "Metastability in the diluted parallel Ising model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(10), pages 1-10, October.
    15. Han Sun & Zhiyun Zha & Chao Huang & Xiaohui Yang, 2025. "Flood disaster industry-linked economic impact and risk assessment: a case study of Yangtze River Economic Zone," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 27(7), pages 15703-15726, July.
    16. Otto, Christian & Willner, Sven Norman & Wenz, Leonie & Frieler, Katja & Levermann, Anders, 2017. "Modeling loss-propagation in the global supply network: The dynamic agent-based model acclimate," OSF Preprints 7yyhd, Center for Open Science.
    17. Song, Bo & Fan, Ziyang & Song, Yurong & Ding, Lei & Qin, Yi & Wang, Xu, 2026. "Network robustness against cascading failures with time-varying adaptive behaviors triggered by information propagation," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    18. Yajun Xiong & Hui Tang & Xiaobo Tian, 2022. "Research on Structural Toughness of Railway City Network in Yellow River Basin and Case Study of Zhengzhou 7–20 Rainstorm Disaster," Sustainability, MDPI, vol. 14(19), pages 1-17, September.
    19. Takayuki Mizuno & Takaaki Ohnishi & Tsutomu Watanabe, 2015. "Structure of global buyer-supplier networks and its implications for conflict minerals regulations," Papers 1505.02274, arXiv.org.
    20. George Van Voorn & Geerten Hengeveld & Jan Verhagen, 2020. "An agent based model representation to assess resilience and efficiency of food supply chains," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-27, November.
    21. Li, WenYao & Xue, Xiaoyu & Pan, Liming & Lin, Tao & Wang, Wei, 2022. "Competing spreading dynamics in simplicial complex," Applied Mathematics and Computation, Elsevier, vol. 412(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:phsmap:v:499:y:2018:i:c:p:142-147. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.