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.


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