Publication
Bifurcation analysis of the γ-Ricker population model using the Lambert W function
| Summary: | In this work, we present the dynamical study and the bifurcation structures of the γ-Ricker population model. Resorting to the Lambert W function, the analytical solutions of the positive fixed point equation for the γ-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 γ-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the γ-Ricker population model is associated with the asymptotic behavior of the Lambert W function in a neighborhood of zero. The theoretical results describe the global and local bifurcations of the γ-Ricker population model, using the Lambert W 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. |
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| Main Authors: | Rocha, J. Leonel |
| Other Authors: | TAHA, Abdel-Kaddous |
| Subject: | γ-Ricker population model Lambert W function Allee effect bifurcation Fold and flip bifurcations Snapback repeller bifurcation Big bang bifurcation |
| Year: | 2020 |
| Country: | Portugal |
| Document type: | article |
| Access type: | restricted access |
| Associated institution: | Universidade Politécnica de Lisboa |
| Language: | English |
| Origin: | Repositório Científico da Universidade Politécnica de Lisboa |
| Summary: | In this work, we present the dynamical study and the bifurcation structures of the γ-Ricker population model. Resorting to the Lambert W function, the analytical solutions of the positive fixed point equation for the γ-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 γ-Ricker population model, which is not a pitchfork bifurcation. Consequently, we prove that the phenomenon of Allee effect for the γ-Ricker population model is associated with the asymptotic behavior of the Lambert W function in a neighborhood of zero. The theoretical results describe the global and local bifurcations of the γ-Ricker population model, using the Lambert W 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. |
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