Generalized r-Lambert Function in the Analysis of Fixed Points and Bifurcations of Homographic 2-Ricker Maps
| Autor: | J. Leonel Rocha, Abdel-Kaddous Taha |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Fixed point Function (mathematics) γ-Ricker population model Nonlinear system symbols.namesake Fold and flip bifurcations Population model Modeling and Simulation Lambert W function Generalized r-Lambert function symbols Quantitative Biology::Populations and Evolution Applied mathematics Cusp point Engineering (miscellaneous) Bifurcation Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1793-6551 0218-1274 |
| Popis: | This paper aims to study the nonlinear dynamics and bifurcation structures of a new mathematical model of the [Formula: see text]-Ricker population model with a Holling type II per-capita birth function, where the Allee effect parameter is [Formula: see text]. A generalized [Formula: see text]-Lambert function is defined on the 3D parameters space to determine the existence and variation of the number of nonzero fixed points of the homographic [Formula: see text]-Ricker maps considered. The singularity points of the generalized [Formula: see text]-Lambert function are identified with the cusp points on a fold bifurcation of the homographic [Formula: see text]-Ricker maps. In this approach, the application of the transcendental generalized [Formula: see text]-Lambert function is demonstrated based on the analysis of local and global bifurcation structures of this three-parameter family of homographic maps. Some numerical studies are included to illustrate the theoretical results. |
| Databáze: | OpenAIRE |
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