Dynamics of a single species under periodic habitat fluctuations and Allee effect

The dynamics of a single species that goes extinct when rare is described by a nonlinear differential equation N′=rN(1−NK)(NK−AK), where a parameter AA (00A>0) and weak (A<0A<0) Allee effects. Thus, we answer questions regarding the location of positive periodic solutions and their stability complementing the research in a recent paper by Padhi et al. [Seshadev Padhi, P.D.N. Srinivasu, G. Kiran Kumar, Periodic solutions for an equation governing dynamics of a renewable resource subjected to Allee effects, Nonlinear Anal. RWA 11 (2010) 2610–2618]. Bounds for periodic solutions and estimates for backward blow-up times are also established. Furthermore, we demonstrate advantages of our approach on a simple example to which the results in the cited paper fail to apply.