Dynamics of a single species under periodic habitat fluctuations and Allee effect (Q420020)

The paper is concerned with the existence of periodic solutions to a first order nonautonomous nonlinear differential equation that models the dynamics of a single species under the influence of the Allee effect. Combining the direction field argument with the method of upper and lower solutions, the authors completely describe population dynamics in the cases of strong (\(A>0\)) and weak (\(A<0\)) Allee effect. They also provide bounds for periodic solutions and estimates for backward blow-up times. Remarkably, a recent general result due to \textit{S. Padhi}, \textit{P. D. N. Srinivasu} and \textit{G. K. Kumar} [Nonlinear Anal., Real World Appl. 11, No. 4, 2610--2618 (2010; Zbl 1197.34078)] does not apply to the simple equation considered as an illustrative example in the paper under review.