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

2009, Volume 6, Issue 4: 701-718. doi: 10.3934/mbe.2009.6.701

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1.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona

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.
- Weinstein Aronszajn determinant,
- Asymptotic stability,
- 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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Abstract

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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