Details
| Original language | English |
|---|---|
| Number of pages | 40 |
| Journal | Journal of Dynamics and Differential Equations |
| Early online date | 5 Feb 2024 |
| Publication status | E-pub ahead of print - 5 Feb 2024 |
Abstract
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the corresponding linearization at an equilibrium determine the latter’s stability or instability. The key ingredient of the proof is the eventual compactness of the semigroup associated with the linearized problem, which is derived by a perturbation argument. The results are illustrated with examples.
Keywords
- Age structure, Diffusion, Linearization, Semigroups, Stability of equilibria
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
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In: Journal of Dynamics and Differential Equations, 05.02.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Stability and Instability of Equilibria in Age-Structured Diffusive Populations
AU - Walker, Christoph
N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL.
PY - 2024/2/5
Y1 - 2024/2/5
N2 - The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the corresponding linearization at an equilibrium determine the latter’s stability or instability. The key ingredient of the proof is the eventual compactness of the semigroup associated with the linearized problem, which is derived by a perturbation argument. The results are illustrated with examples.
AB - The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the corresponding linearization at an equilibrium determine the latter’s stability or instability. The key ingredient of the proof is the eventual compactness of the semigroup associated with the linearized problem, which is derived by a perturbation argument. The results are illustrated with examples.
KW - Age structure
KW - Diffusion
KW - Linearization
KW - Semigroups
KW - Stability of equilibria
UR - http://www.scopus.com/inward/record.url?scp=85184234269&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2304.09589
DO - 10.48550/arXiv.2304.09589
M3 - Article
AN - SCOPUS:85184234269
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
SN - 1040-7294
ER -