Singular Homoclinic Bifurcations in Tri-trophic Food Chains

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/4249 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/4249 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/4249 archive 351 disk0/00/00/49/51 2016-01-15 02:07:51 2021-08-27 17:15:45 2016-01-15 02:07:51 monograph show 2 Feo O. de Rinaldi S. 7286 Singular Homoclinic Bifurcations in Tri-trophic Food Chains pub iis_met iis_mod iis_sys prog_dyn The Rosenzweig-MacArthur food chain model is proved to have homoclinic orbits. The proof is in two steps. First we use a geometric approach based on singular perturbation and detect singular homoclinic orbits as well as parameter combinations for which these orbits exist. Then we show, numerically, that for slightly different parameter values there exist also non singular homoclinic orbits which tend toward the singular ones when the time responses of the three trophic levels are extremely diversified. The analysis is performed systematically, without exploiting too deeply the mathematical structure of the Rosenzweig-MacArthur model. This is done intentionally, in order to facilitate readers interested more in the methodology than in the application to food chains. 1996-07 published WP-96-076 WP-96-076 10 253 public working_paper IIASA, Laxenburg, Austria 32 FALSE info:eu-repo/semantics/book