Organizing center for the bifurcation analysis of a generalized Gause model with prey harvesting and Holling response function of type III
| Autor: | Christiane Rousseau, Sophie Laurin |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Hopf bifurcation
Pure mathematics Applied Mathematics 010102 general mathematics Mathematical analysis Saddle-node bifurcation Nilpotent saddle bifurcation Bifurcation diagram 01 natural sciences 010101 applied mathematics symbols.namesake Pitchfork bifurcation Transcritical bifurcation Bifurcation theory Holling response function of type III symbols Homoclinic bifurcation Bogdanov–Takens bifurcation 0101 mathematics Generalized Gause model with prey harvesting Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 251(10):2980-2986 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2011.04.017 |
| Popis: | The present note is an addendum to the paper of Etoua–Rousseau (2010) [1] which presented a study of a generalized Gause model with prey harvesting and a generalized Holling response function of type III: p ( x ) = m x 2 a x 2 + b x + 1 . Complete bifurcation diagrams were proposed, but some parts were conjectural. An organizing center for the bifurcation diagram was given by a nilpotent point of saddle type lying on an invariant line and of codimension greater than or equal to 3. This point was of codimension 3 when b ≠ 0 , and was conjectured to be of infinite codimension when b = 0 . This conjecture was in line with a second conjecture that the Hopf bifurcation of order 2 degenerates to a Hopf bifurcation of infinite codimension when b = 0 . In this note we prove these two conjectures. |
| Databáze: | OpenAIRE |
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