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

Sílvia Cuadrado

doi:10.3934/mbe.2009.6.701

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

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

Sílvia Cuadrado^1,

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

Received: January 31, 2009

Revised: June 30, 2009

Published: August 2009

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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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Mathematics Subject Classification: Primary: 47A10, 92D15; Secondary: 35B35.

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