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

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

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

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

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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Keywords Weinstein Aronszajn determinant; Asymptotic stability; evolutionarily stable strategy.

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

 

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