Dynamics of a single species under periodic habitat fluctuations and Allee effect. (English) Zbl 1239.37013

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 S. Padhi, P. D. N. Srinivasu and 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.


37N25 Dynamical systems in biology
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations


Zbl 1197.34078
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