Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T07:06:22.536Z Has data issue: false hasContentIssue false
  • English
  • Français

Long-Time Simulation of a Size-Structured Population Model witha Dynamical Resource

Published online by Cambridge University Press:  08 April 2010

L. M. Abia ,
O. Angulo ,
J. C. López-Marcos  and
M. A. López-Marcos
L. M. Abia
Affiliation:
Departamento de Matemática Aplicada. Facultad de Ciencias Universidad de Valladolid, Paseo Prado de la Magdalena sn., 47005. Valladolid. Spain
O. Angulo
Affiliation:
Departamento de Matemática Aplicada, Escuela Universitaria Politécnica Universidad de Valladolid, C/ Fco. Mendizabal 1, 47014 Valladolid, Spain
J. C. López-Marcos
Affiliation:
Departamento de Matemática Aplicada. Facultad de Ciencias Universidad de Valladolid, Paseo Prado de la Magdalena sn., 47005. Valladolid. Spain
M. A. López-Marcos*
Affiliation:
Departamento de Matemática Aplicada. Facultad de Ciencias Universidad de Valladolid, Paseo Prado de la Magdalena sn., 47005. Valladolid. Spain
*
* Corresponding author. E-mail: [email protected]
Get access

Abstract

In this paper, we study the numerical approximation of a size-structured population modelwhose dependency on the environment is managed by the evolution of a vital resource. Weshow that this is a difficult task: some numerical methods are not suitable for along-time integration. We analyze the reasons for the failure.

Keywords

size-structured population modeldynamical resourcenumerical methods
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 6: Ecology (Part 2) , 2010 , pp. 1 - 21
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abia, L. M., Angulo, O., López-Marcos, J. C.. Age-structured population dynamics models and their numerical solutions . Ecol. Model., 188 (2005), 112–136. CrossRefGoogle Scholar
Abia, L. M., Angulo, O., López-Marcos, J. C.. Size-structured population dynamics models and their numerical solutions . Discrete Contin. Dyn. Syst. B, 4 (2004), 1203–1222. Google Scholar
Abia, L.M., Angulo, O., López-Marcos, J.C. López-Marcos., M.A. Numerical schemes for a size-structured cell population model with equal fission . Mat. Computer Model., 50 (2009), 653–664.CrossRefGoogle Scholar
Adimy, M., Angulo, O., Crauste, F. López-Marcos., J.C. Numerical integration of a mathematical model of hematopoietic stem cell dynamics . Computers and Math. Applic., 56 (2008), 594–606.CrossRefGoogle Scholar
Angulo, O. López-Marcos., J. C. Numerical integration of fully nonlinear size-structured models . Appl. Numer. Math., 50 (2004), 291–327.CrossRefGoogle Scholar
Bees, M.A., Angulo, O., López-Marcos, J.C., Schley, D.. Dynamics of a structured slug population model in the absence of seasonal variation . Math. Mod. Meth. in Appl. Sci., 16 (2006), 1961–1985. CrossRefGoogle Scholar
J.M. Cushing. An Introduction to Structured Populations Dynamics. CMB-NSF Regional Conference Series in Applied Mathematics. SIAM, 1998.
M. Iannelli. Mathematical Theory of Age-Structured Population Dynamics. Applied Mathematics Monographs. C.N.R., Giardini Editori e Stampatori, Pisa, 1995.
Iannelli, M., Kostova, T., Milner, F.A.. A fourth-order method for numerical integration of age- and size-structured population models . Numer. Methods Partial Differential Equations, 25 (2009) 918–930. CrossRefGoogle Scholar
Kooijman, S.A.L.M, Metz, J.A.J.. On the dynamics of chemically stressed populations: the deduction of a population consequences from effects on individuals . Ecotox. Environ. Saf., 8 (1984), 254–274. CrossRefGoogle ScholarPubMed
J.A.J. Metz and E.O. Dieckmann, editors. The Dynamics of Physiologically Structured Populations. Springer Lecture Notes in Biomathematics, 68. Springer, Heildelberg, 1986.
B. Perthame. Transport Equations in Biology. Birkhäuser Verlag, Basel, 2007.
de Roos., A.M. Numerical methods for structured population models: The escalator boxcar train . Numer. Methods Partial Differential Equations, 4 (1988), 173–195.CrossRefGoogle Scholar
Shen, J., Shu, C.W. Zhang, M.P.. A high order WENO scheme for a hierarchical size-structured population model . J. Sci. Comput., 33 (2007), 279–291.CrossRefGoogle Scholar
G.F. Webb. Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker, eds, New York, 1985.