IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v522y2026ics0096300326000469.html

Revisiting deterministic evolution: Robustness of cooperation under stochastic mutations and delayed feedback

Author

Listed:
  • Hu, Kaipeng
  • Zhao, Xiaoqian
  • Li, Zhouhong
  • Özer, Mahmut
  • Shi, Lei
  • Perc, Matjaž

Abstract

Stochastic mutations are intrinsic to evolutionary processes, reflecting both random genetic variation and broader uncertainties in strategic behavior. Here we extend our previous work on delayed evolutionary dynamics in a two species system by introducing Gaussian stochastic mutations into replicator equations with time delays. This framework captures both intra and interspecific interactions, with delays representing inevitable lags in feedback and response in biological and social systems. Using Lyapunov based stability analysis and numerical simulations, we show that while stochasticity mutations transient trajectories, cooperative equilibria remain robust even under very strong noise, with only extreme perturbations leading to divergence. These findings demonstrate that deterministic models retain strong predictive power for long term evolutionary outcomes across realistic conditions, offering new insights into how memory and randomness jointly shape the evolution of cooperation.

Suggested Citation

  • Hu, Kaipeng & Zhao, Xiaoqian & Li, Zhouhong & Özer, Mahmut & Shi, Lei & Perc, Matjaž, 2026. "Revisiting deterministic evolution: Robustness of cooperation under stochastic mutations and delayed feedback," Applied Mathematics and Computation, Elsevier, vol. 522(C).
    • Handle: RePEc:eee:apmaco:v:522:y:2026:i:c:s0096300326000469
    DOI: 10.1016/j.amc.2026.129994
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300326000469
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2026.129994?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.

    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:apmaco:v:522:y:2026:i:c:s0096300326000469. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.