Non-autonomous periodic systems with Allee effects

• Autor(a) principal: Luís, Rafael
• Data de Publicação: 2010
• Outros Autores: Elaydi, Saber, Oliveira, Henrique
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.13/3775
• topic: Unimodal Allee maps; Threshold point; Carrying capacity; Composition map; Stability; Bifurcation; .; Faculdade de Ciências Exatas e da Engenharia

A new class of maps called unimodal Allee maps are introduced. Such maps arise in the study of population dynamics in which the population goes extinct if its size falls below a threshold value. A unimodal Allee map is thus a unimodal map with three fixed points, a zero fixed point, a small positive fixed point, called threshold point, and a bigger positive fixed point, called the carrying capacity. In this paper, the properties and stability of the three fixed points are studied in the setting of non-autonomous periodic dynamical systems or difference equations. Finally, we investigate the bifurcation of periodic systems/difference equations when the system consists of two unimodal Allee maps.