Stability of equilibria of a predator-prey model of phenotype evolution

  • Received: 01 February 2009 Accepted: 29 June 2018 Published: 01 September 2009
  • MSC : Primary: 47A10, 92D15; Secondary: 35B35.

  • We consider a selection mutation predator-prey model for the distribution of individuals with respect to an evolutionary trait. Local stability of the equilibria of this model is studied using the linearized stability principle and taking advantage of the (assumed) asymptotic stability of the equilibria of the resident population adopting an evolutionarily stable strategy.

    Citation: Sílvia Cuadrado. Stability of equilibria of a predator-prey model of phenotype evolution[J]. Mathematical Biosciences and Engineering, 2009, 6(4): 701-718. doi: 10.3934/mbe.2009.6.701

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  • We consider a selection mutation predator-prey model for the distribution of individuals with respect to an evolutionary trait. Local stability of the equilibria of this model is studied using the linearized stability principle and taking advantage of the (assumed) asymptotic stability of the equilibria of the resident population adopting an evolutionarily stable strategy.


  • This article has been cited by:

    1. King-Yeung Lam, Stability of Dirac concentrations in an integro-PDE model for evolution of dispersal, 2017, 56, 0944-2669, 10.1007/s00526-017-1157-1
    2. Azmy S. Ackleh, Baoling Ma, Paul L. Salceanu, Persistence and global stability in a selection–mutation size-structured model, 2011, 5, 1751-3758, 436, 10.1080/17513758.2010.538729
    3. Jan-Erik Busse, Sílvia Cuadrado, Anna Marciniak-Czochra, Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation, 2022, 84, 0303-6812, 10.1007/s00285-021-01708-w
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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