Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example

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published 79464 2 219465 document 79464 lightbox.jpg image/png 57695c43469a9fd03c4da53719e74028 MD5 31246 2017-10-12 11:54:39 https://pure.iiasa.ac.at/id/eprint/9250/2/lightbox.jpg 9250 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/79463 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/79463 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/79463 archive 351 disk0/00/00/92/50 2016-01-15 08:44:03 2021-08-27 17:21:18 2016-01-15 08:44:03 article show 1 Diekmann O. Gyllenberg M. Metz J.A.J. 7506 Nakaoka S. de Roos A.M. Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example pub iis_ecl prog_eep Physiologically structured population models; Size-structure; Delay equations; Linearised sability; Characteristic equation We consider the interaction between a general size-structured consumer population and an unstructured resource. We show that stability properties and bifurcation phenomena can be understood in terms of solutions of a system of two delay equations (a renewal equation for the consumer population birth rate coupled to a delay differetial equation for the resource concentration). As many results for such systems are available, we can draw rigorous conclusions concerning dynamical behaviour from an analysis of a characteristic equation. We derive the characteristic equation for a fairly general class of population models, including those based on the Kooijman-Metz Daphnia model and a model introduced by Gurney-Nisbet and Jones et al., and next obtain various ecological insights by analytical or numerical studies of special cases. 2010-08 published Springer 10.1007/s00285-009-0299-y XJ-10-055 [doi:10.1007/s00285-009-0299-y] 206 public Journal of Mathematical Biology 61 2 277-318 TRUE 1432-1416 http://pure.iiasa.ac.at/14731/ publ FALSE info:eu-repo/semantics/article