Stability and Instability of Equilibria in Age-Structured Diffusive Populations
- Resource Type
- Original Paper
- Authors
- Walker, Christoph
- Source
- Journal of Dynamics and Differential Equations. :1-40
- Subject
- Age structure
Diffusion
Semigroups
Stability of equilibria
Linearization
47D06
35B35
35M10
92D25
- Language
- English
- ISSN
- 1040-7294
1572-9222
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.