Details
| Originalsprache | Englisch |
|---|---|
| Seitenumfang | 40 |
| Fachzeitschrift | Journal of Dynamics and Differential Equations |
| Frühes Online-Datum | 5 Feb. 2024 |
| Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
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in: Journal of Dynamics and Differential Equations, 05.02.2024.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -