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


  • Moreira, Helmar Nunes
  • Araujo, Ricardo Azevedo


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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    References listed on IDEAS

    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," Review of Economic Studies, Oxford University Press, 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, January.
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    More about this item


    limit cycles; evolutionary game theory; Kukles system; Dulac-Cherkas function;

    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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