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Analysis of quasi-dynamic ordinary differential equations and the quasi-dynamic replicator

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  • Griffin, Christopher
  • Jiang, Libo
  • Wu, Rongling

Abstract

We study the mathematical properties of the quasi-dynamic ordinary differential equations defined empirically in Chen et al. (2019). In particular, we show how the allometric scaling mentioned in that work emerges naturally from the generalized Lotka–Volterra model under the quasi-dynamic ordinary differential equations paradigm. We then define and study the proportional quasi-dynamic ordinary differential equations and discuss the relationship of this equation system to both the classical and discrete time replicator dynamics. We prove asymptotic properties of these systems for large and small populations and show that there exist populations for which the proportion of the population varies cyclically as a function of total logarithmic population size.

Suggested Citation

  • Griffin, Christopher & Jiang, Libo & Wu, Rongling, 2020. "Analysis of quasi-dynamic ordinary differential equations and the quasi-dynamic replicator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120301679
    DOI: 10.1016/j.physa.2020.124422
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    References listed on IDEAS

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    1. repec:hhs:iuiwop:487 is not listed on IDEAS
    2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    3. Friedman, Daniel & Sinervo, Barry, 2016. "Evolutionary Games in Natural, Social, and Virtual Worlds," OUP Catalogue, Oxford University Press, number 9780199981151.
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