Details
Original language | English |
---|---|
Pages (from-to) | 1315-1354 |
Number of pages | 40 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 37 |
Issue number | 2 |
Early online date | 5 Feb 2024 |
Publication status | Published - Jun 2025 |
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
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Dynamics and Differential Equations, Vol. 37, No. 2, 06.2025, p. 1315-1354.
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 - Publisher Copyright: © 2024, The Author(s).
PY - 2025/6
Y1 - 2025/6
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 - 10.1007/s10884-023-10340-9
DO - 10.1007/s10884-023-10340-9
M3 - Article
AN - SCOPUS:85184234269
VL - 37
SP - 1315
EP - 1354
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
SN - 1040-7294
IS - 2
ER -