Dynamics and bifurcations of a map of homographic Ricker type

• Autor(a) principal: Rocha, J. Leonel
• Data de Publicação: 2020
• Outros Autores: TAHA, Abdel-Kaddous, Fournier-Prunaret, D.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.21/12660
• topic: Ricker map; Homographic map; Lambert W function; Fold and flip bifurcations; Big bang bifurcation; Cusp point

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.