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| Content Provider | Springer Nature Link |
|---|---|
| Author | Roos, A. M. Diekmann, O. Getto, P. Kirkilionis, M. A. |
| Copyright Year | 2009 |
| 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. |
| Starting Page | 259 |
| Ending Page | 297 |
| Page Count | 39 |
| File Format | |
| ISSN | 00928240 |
| Journal | Bulletin of Mathematical Biology |
| Volume Number | 72 |
| Issue Number | 2 |
| e-ISSN | 15229602 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2009-07-31 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Numerical equilibrium analysis Structured populations Stability boundaries Hopf bifurcation Consumer resource models Delay equations Renewal equations Delay differential equations Daphnia models Cell Biology Life Sciences Mathematical Biology in General |
| Content Type | Text |
| Resource Type | Article |
| Subject | Neuroscience Biochemistry, Genetics and Molecular Biology Mathematics Pharmacology Immunology Computational Theory and Mathematics Environmental Science Agricultural and Biological Sciences |
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