Explosion birth and extinction: double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models
| Autor: | J. Leonel Rocha, Abdel-Kaddous Taha, Daniele Fournier-Prunaret |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Physics
Big Bang Extinction Population dynamics Applied Mathematics Tsoularis-Wallace's growth models Parameter space Type (model theory) Allee effect symbols.namesake Theoretical physics Bifurcation analysis Fold and flip bifurcations Big bang bifurcations symbols Quantitative Biology::Populations and Evolution Discrete Mathematics and Combinatorics Statistical physics Bifurcation |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called ``box-within-a-box'' type. The double big bang bifurcations are related to the existence of flip codimension--2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena. |
| Databáze: | OpenAIRE |
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