Non-autonomous periodic systems with Allee effects

Rafael Luís, Saber Elaydi, Henrique Oliveira
2010 Journal of difference equations and applications (Print)  
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
more » ... ed 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.
doi:10.1080/10236190902794951 fatcat:qc3rcs7bjrhutmp6emp6dc7dxu