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

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2009, 6(4): 701-718. doi: 10.3934/mbe.2009.6.701

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

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

Received February 2009 Revised July 2009 Published September 2009

Abstract
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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.

Keywords: Weinstein Aronszajn determinant, Asymptotic stability, evolutionarily stable strategy..

Mathematics Subject Classification: Primary: 47A10, 92D15; Secondary: 35B3.

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

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