Bifurcation analysis of the γ-Ricker population model using the Lambert W function
| Autor: | J. Leonel Rocha, Abdel-Kaddous Taha |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Work (thermodynamics)
Applied Mathematics Allee effect bifurcation Lambert W function γ-Ricker population model symbols.namesake Bifurcation analysis Fold and flip bifurcations Population model Modeling and Simulation symbols Quantitative Biology::Populations and Evolution Applied mathematics Big bang bifurcation Snapback repeller bifurcation Engineering (miscellaneous) Bifurcation Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | In this work, we present the dynamical study and the bifurcation structures of the [Formula: see text]-Ricker population model. Resorting to the Lambert [Formula: see text] function, the analytical solutions of the positive fixed point equation for the [Formula: see text]-Ricker population model are explicitly presented and conditions for the existence and stability of these fixed points are established. The main focus of this work is the definition and characterization of the Allee effect bifurcation for the [Formula: see text]-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the [Formula: see text]-Ricker population model is associated with the asymptotic behavior of the Lambert [Formula: see text] function in a neighborhood of zero. The theoretical results describe the global and local bifurcations of the [Formula: see text]-Ricker population model, using the Lambert [Formula: see text] function in the presence and absence of the Allee effect. The Allee effect, snapback repeller and big bang bifurcations are investigated in the parameters space considered. Numerical studies are included. |
| Databáze: | OpenAIRE |
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