Abstract
An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 705-729 |
| Number of pages | 25 |
| Journal | Journal of mathematical biology |
| Volume | 32 |
| Issue number | 7 |
| DOIs | |
| State | Published - Aug 1994 |
Keywords
- Age-structured population dynamics
- Asymptotic dynamics
- Cannibalism
- Existence/uniqueness
- Global stability
- Hierarchical models
- Intra-specific competition
- McKendrick equations
ASJC Scopus subject areas
- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics