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On the existence and the number of limit cycles in evolutionary games

Author

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  • Moreira, Helmar Nunes
  • Araujo, Ricardo Azevedo

Abstract

In this paper it is shown that an extended evolutionary system proposed by Hofbauer and Sigmund (1998) may be transformed into a Kukles system. Then a Dulac-Cherkas function related to the Kukles system is derived, which allows us to determine the number of limit cycles or its non-existence.

Suggested Citation

  • Moreira, Helmar Nunes & Araujo, Ricardo Azevedo, 2011. "On the existence and the number of limit cycles in evolutionary games," MPRA Paper 33895, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:33895
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    File URL: https://mpra.ub.uni-muenchen.de/33895/1/MPRA_paper_33895.pdf
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    References listed on IDEAS

    as
    1. W. W. Chang & D. J. Smyth, 1971. "The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 37-44.
    2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
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    More about this item

    Keywords

    limit cycles; evolutionary game theory; Kukles system; Dulac-Cherkas function;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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