Non-autonomous periodic systems with Allee effects

作者：Luis Rafael^*; Elaydi Saber; Oliveira Henrique

来源：Journal of Difference Equations and Applications, 2010, 16(10): 1179-1196.

DOI：10.1080/10236190902794951

• unimodal Allee maps
• threshold point
• carrying capacity
• composition map
• stability
• bifurcation

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.

• 出版日期2010