Abstract
In this paper, we discuss the qualitative behavior of an age/size-structured population equation with delay in the birth process. The linearization about stationary solutions is analyzed by semigroup and spectral methods. In particular, the spectrally determined growth property of the linearized semi-group is derived from its long-term regularity. These analytical results allow us to derive linearized stability and instability results under some conditions. The principal stability criterions are given in terms of a modified net reproduction rate. Finally, two examples are presented and simulated to illustrated the obtained conclusions.
| Original language | English |
|---|---|
| Pages (from-to) | 109-131 |
| Number of pages | 23 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 18 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2013 |
Keywords
- C -semigroup
- Delayed boundary condition
- Linearized stability
- Size-structured population model
- Spectral analysis