Asymptotic behaviour of a semilinear age-structured population model with a dynamics for the resource
type: Item
instance of: scholarly article
title: Asymptotic behaviour of a semilinear age-structured population model with a dynamics for the resource
zbMATH Open document ID: 1012.35083
DOI: 10.1016/S0895-7177(01)00174-1
published in: Mathematical and Computer Modelling
publication date: 2002-08-15T00:00:00Z
review text: The authors investigate a population model of the form \[ \begin{cases} u_t+u_a = -m_1(r)u,\\ v^1 = u(\ell,t)-m_2(r)v,\\ r^1 = \biggl(g(r)-H \bigl[ L(u,v)\bigr] \biggr)r,\\ {\phantom =} u(0,t)=bv(t),\;u(a,0)= u_0(a),\;v(0)=v_0,\;r(0) =r_0. \end{cases} \tag{1} \] Here, the age \(a\in(0,\ell)\), \(\ell=\) maturation age, \(m_1 (r)\), \(m_2(r)=\) death rates, \(m_1\), for juveniles, \(m_2\) for adults. The second equation in (1) describes the transition rate from juveniles to adults. The third equation describes the dynamics of the resource \(r(t)\). The authors use semigroup theory to prove existence, uniqueness and continuous dependence on initial age distributions. Stability of equilibrium solutions and bifurcation is also discussed in depth and complemented with numerical results.
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1781898
zbMATH Keywords: stability
zbMATH Keywords: population model
zbMATH Keywords: semigroup theory
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence
zbMATH Keywords: bifurcation
zbMATH Keywords: numerical results
author: Ángel Calsina
author: O. El idrissi
reviewed by: René Sperb
MaRDI profile type: Publication
cites work: Non-linear age-dependent population dynamics
cites work: Q3220397
cites work: Q4723599
cites work: Q4386706
cites work: Q4039920
cites work: Asymptotic behavior of an age-structured population model and optimal maturation age
cites work: Global Dynamics and Optimal Life History of a Structured Population Model
cites work: Stability analysis for equilibria in age-specific population dynamics
cites work: Delay equations. Functional-, complex-, and nonlinear analysis
cites work: Q3477543
cites work: Q4010833
cites work: On the formulation and analysis of general deterministic structured population models. I: Linear theory
cites work: On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: A model of physiologically structured population dynamics with a nonlinear individual growth rate
cites work: One-parameter semigroups of positive operators
cites work: Q3994744
cites work: Q3850160
cites work: Geometric theory of semilinear parabolic equations
cites work: Q3240942
cites work: Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
cites work: Q4748596
cites work: Q3254057
cites work: Bifurcation, perturbation of simple eigenvalues, and linearized stability
cites work: Q5526485
cites work: A continuous, age-structured insect population model
cites work: Discrete delay, distributed delay and stability switches
cites work: Q3995025
full work available at URL: s0895-7177(01)00174-1
OpenAlex ID: W2142226426
description: scientific article; zbMATH DE number 1781898