On the net reproduction rate of continuous structured populations with distributed states at birth
arXiv:1202.3800 · doi:10.1016/j.camwa.2013.04.010
Abstract
We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral properties of a parametrized family of unbounded operators. The alternative approach, on which we focus here, is based on the reformulation of the problem as an integral equation. In this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity. Finally, we briefly discuss a third approach, which is based on the finite rank approximation of the recruitment operator.
To appear in Computers and Mathematics with Applications
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Cited by in corpus (6)
- Structured populations with distributed recruitment: from PDE to delay formulation
- Modelling effects of rapid evolution on persistence and stability in structured predator-prey systems
- Positive steady states of evolution equations with finite dimensional nonlinearities
- Net reproduction functions for nonlinear structured population models
- Finite difference approximations for a size-structured population model with distributed states in the recruitment
- Asymptotic behaviour of a structured population model on a space of measures