Skip to main content
Article thumbnail
Location of Repository

A Nonlocal Reaction-Diffusion Model for a Single Species with Stage Structure and Distributed Maturation Delay

By J F Al-Omari and S A Gourley

Abstract

<p>We propose a delay differential equation model for a single species with stage-structure in which the maturation delay is modelled as a distribution, to allow for the possibility that individuals may take different amounts of time to mature. General birth and death rate functions are used. We find that the dynamics of the model depends largely on the qualitative form of the birth function, which depends on the total number of adults. If it is monotonic increasing and a non-zero equilibrium exists, then the equilibrium is globally stable for all maturation delay distributions with compact support. For the case of a finite spatial domain with impermeable boundaries, a reaction-diffusion extension of the model is rigorously derived using an approach based on the von Foerster diffusion equation. The resulting reaction-diffusion system is nonlocal. The dynamics of the reaction-diffusion system again depends largely on the qualitative form of the birth function. If the latter is nonmonotone with a single hump, then the dynamics depends largely on whether the equilibrium is to the left or right of the hump, with oscillatory dynamics a possibility if it is sufficiently far to the right.</p

Year: 2005
DOI identifier: 10.1017/S0956792504005716
OAI identifier: oai:epubs.surrey.ac.uk:282

Suggested articles

Citations

  1. (1990). A time-delay model of single species growth with stage structure. doi
  2. (1990). Abstract functional differential equations and reactiondiffusion systems.
  3. (1984). Asymptotic stability for some systems of semilinear Volterra diffusion equations. doi
  4. (1995). Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions. doi
  5. (1995). Monotone Dynamical Systems: An introduction to the theory of competitive and cooperative systems. doi
  6. (1980). Nicholson’s blowflies revisited. doi
  7. (1982). On a certain class of semilinear Volterra diffusion equations. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.