Dynamics and bifurcations of a map of homographic Ricker type
| Autor: | Danièle Fournier-Prunaret, Abdel-Kaddous Taha, J. Leonel Rocha |
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| Rok vydání: | 2020 |
| Předmět: |
Aerospace Engineering
Ocean Engineering Fixed point Dynamical system 01 natural sciences Stability (probability) Lambert W function Homographic map symbols.namesake 0103 physical sciences Quantitative Biology::Populations and Evolution Applied mathematics Big bang bifurcation Electrical and Electronic Engineering 010301 acoustics Bifurcation Mathematics Cusp (singularity) Ricker map Applied Mathematics Mechanical Engineering Function (mathematics) Nonlinear system Fold and flip bifurcations Control and Systems Engineering symbols Cusp point |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1573-269X 0924-090X |
| Popis: | A dynamical system of the type homographic Ricker map is considered; this is a particular case of a new extended $$\gamma $$ -Ricker population model with a Holling type II per-capita birth function. The purpose of this paper is to investigate the nonlinear dynamics and bifurcation structure of the proposed model. The existence, nature and stability of the fixed points of the homographic Ricker map are analyzed, by using a Lambert W function. Fold and flip bifurcation structures of the homographic Ricker map are investigated, in which there are flip codimension-2 bifurcation points and cusp points, while some parameters evolve. Some communication areas and big bang bifurcation curves are also detected. Numerical studies are included. |
| Databáze: | OpenAIRE |
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