Bifurcation structures in a 2D exponential diffeomorphism with Allee effect
| Autor: | J. Leonel Rocha, Abdel-Kaddous Taha |
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| Rok vydání: | 2019 |
| Předmět: |
Contour line
Linha de contorno Aerospace Engineering Ocean Engineering Fixed point 01 natural sciences Stability (probability) symbols.namesake Diffeomorphisms 0103 physical sciences Quantitative Biology::Populations and Evolution Electrical and Electronic Engineering 010301 acoustics Bifurcation Mathematics Allee effect Cusp (singularity) Allee’s effect bifurcation Applied Mathematics Mechanical Engineering Mathematical analysis Exponential function Fold and flip bifurcations Control and Systems Engineering Dobrar e virar bifurcações symbols Embedding Diffeomorphism |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1573-269X 0924-090X |
| DOI: | 10.1007/s11071-019-04759-3 |
| Popis: | An embedding of one-dimensional generic growth functions into a two-dimensional diffeomorphism is considered. This family of unimodal maps naturally incorporates a key item of ecological and biological research: the Allee effect. Consequently, the presence of this species extinction phenomenon leads us to a new definition of bifurcation for this two-dimensional exponential diffeomorphism: Allee’s effect bifurcation. The stability and the nature of the fixed points of the two-dimensional diffeomorphism are analyzed, by studying the corresponding contour lines. Fold and flip bifurcation structures of this exponential diffeomorphism are investigated, in which there are flip codimension-2 bifurcation points and cusp points, when some parameters evolve. Numerical studies are included. |
| Databáze: | OpenAIRE |
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