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Numerical equilibrium analysis for structured consumer resource models
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Roos, A. M. de, Diekmann, O., Getto, P. and Kirkilionis, Markus (2010) Numerical equilibrium analysis for structured consumer resource models. Bulletin of Mathematical Biology, Vol.72 (No.2). pp. 259-297. doi:10.1007/s11538-009-9445-3 ISSN 0092-8240.
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Official URL: http://dx.doi.org/10.1007/s11538-009-9445-3
Abstract
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for “Daphnia consuming algae” models in C-code. The results obtained by way of this implementation are shown in the form of graphs.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Age-structured populations, Delay differential equations, Consumers -- Mathematical models, Daphnia -- Mathematical models | ||||
Journal or Publication Title: | Bulletin of Mathematical Biology | ||||
Publisher: | Springer New York LLC | ||||
ISSN: | 0092-8240 | ||||
Official Date: | February 2010 | ||||
Dates: |
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Volume: | Vol.72 | ||||
Number: | No.2 | ||||
Number of Pages: | 29 | ||||
Page Range: | pp. 259-297 | ||||
DOI: | 10.1007/s11538-009-9445-3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
Data sourced from Thomson Reuters' Web of Knowledge
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