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Permanence in Polymatrix Replicators

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  • Telmo Peixe

Abstract

Generally a biological system is said to be permanent if under small perturbations none of the species goes to extinction. In 1979 P. Schuster, K. Sigmund, and R. Wolff [14] introduced the concept of permanence as a stability notion for systems that models the self-organization of biological macromolecules. After, in 1987 W. Jansen [8], and J. Hofbauer and K. Sigmund [5] give sufficient conditions for permanence in the usual replicators. In this paper we extend these results for polymatrix replicators.

Suggested Citation

  • Telmo Peixe, 2019. "Permanence in Polymatrix Replicators," Working Papers REM 2019/69, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    • Handle: RePEc:ise:remwps:wp0692019
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    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_069_2019.pdf
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    Cited by:

    1. Telmo Peixe & Alexandre A. Rodrigues, 2022. "Stability of heteroclinic cycles: a new approach," Papers 2204.00848, arXiv.org.
    2. Telmo Peixe & Alexandre A. Rodrigues, 2021. "Persistent Strange attractors in 3D Polymatrix Replicators," Papers 2103.11242, arXiv.org, revised Jan 2022.

    More about this item

    Keywords

    Permanence; Polymatrix Replicator; Stability; Replicator equation; Evolutionary game theory; Lotka-Volterra.;
    All these keywords.

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