Document Type
Post-Print
Publication Date
10-2010
Abstract
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 tree 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 nonautonomous 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.
Identifier
10.1080/10236190902794951
Repository Citation
Luís, R., Elaydi, S., & Oliveira, H. (2010). Non-autonomous periodic systems with Allee effects. Journal of Difference Equations and Applications, 16(10), 1179-1196. http://doi.org/10.1080/10236190902794951
Publication Information
Journal of Difference Equations and Applications