Asymptotic stability of equilibria of selection-mutation equations

Àngel Calsina; Sílvia Cuadrado

doi:https://doi.org/10.1007/s00285-006-0056-4

Asymptotic stability of equilibria of selection-mutation equations

Àngel Calsina, Sílvia Cuadrado

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

15 Citations (Scopus)

Abstract

We study local stability of equilibria of selection-mutation equations when mutations are either very small in size or occur with very low probability. The main mathematical tools are the linearized stability principle and the fact that, when the environment (the nonlinearity) is finite dimensional, the linearized operator at the steady state turns out to be a degenerate perturbation of a known operator with spectral bound equal to 0. An example is considered where the results on stability are applied. © Springer-Verlag 2007.

Original language	English
Pages (from-to)	489-511
Journal	Journal of Mathematical Biology
Volume	54
DOIs	https://doi.org/10.1007/s00285-006-0056-4
Publication status	Published - 1 Apr 2007

Keywords

Asymptotic stability
Selection-mutation equation
Weinstein-Aronszajn determinant

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abstract = "We study local stability of equilibria of selection-mutation equations when mutations are either very small in size or occur with very low probability. The main mathematical tools are the linearized stability principle and the fact that, when the environment (the nonlinearity) is finite dimensional, the linearized operator at the steady state turns out to be a degenerate perturbation of a known operator with spectral bound equal to 0. An example is considered where the results on stability are applied. {\textcopyright} Springer-Verlag 2007.",

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AU - Cuadrado, Sílvia

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N2 - We study local stability of equilibria of selection-mutation equations when mutations are either very small in size or occur with very low probability. The main mathematical tools are the linearized stability principle and the fact that, when the environment (the nonlinearity) is finite dimensional, the linearized operator at the steady state turns out to be a degenerate perturbation of a known operator with spectral bound equal to 0. An example is considered where the results on stability are applied. © Springer-Verlag 2007.

AB - We study local stability of equilibria of selection-mutation equations when mutations are either very small in size or occur with very low probability. The main mathematical tools are the linearized stability principle and the fact that, when the environment (the nonlinearity) is finite dimensional, the linearized operator at the steady state turns out to be a degenerate perturbation of a known operator with spectral bound equal to 0. An example is considered where the results on stability are applied. © Springer-Verlag 2007.

KW - Asymptotic stability

KW - Selection-mutation equation

KW - Weinstein-Aronszajn determinant

U2 - https://doi.org/10.1007/s00285-006-0056-4

DO - https://doi.org/10.1007/s00285-006-0056-4

M3 - Article

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SP - 489

EP - 511

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