Mathematical Biosciences and Engineering, 2015, 12(1): 83-97. doi: 10.3934/mbe.2015.12.83.

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Delayed population models with Allee effects and exploitation

1. Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidade de Vigo, Campus Marcosende, 36310 Vigo
2. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., H-6720 Szeged

Allee effects make populations more vulnerable to extinction, especially under severe harvesting or predation. Using a delay-differential equation modeling the evolution of a single-species population subject to constant effort harvesting, we show that the interplay between harvest strength and Allee effects leads not only to collapses due to overexploitation; large delays can interact with Allee effects to produce extinction at population densities that would survive for smaller time delays.In case of bistability, our estimations on the basins of attraction of the two coexisting attractors improve some recent results in this direction. Moreover, we show that the persistent attractor can exhibit bubbling: a stable equilibrium loses its stability as harvesting effort increases, giving rise to sustained oscillations, but higher mortality rates stabilize the equilibrium again.
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Keywords bifurcation.; bistability; difference equation; global stability; delay differential equation; Allee effect; Population model

Citation: Eduardo Liz, Alfonso Ruiz-Herrera. Delayed population models with Allee effects and exploitation. Mathematical Biosciences and Engineering, 2015, 12(1): 83-97. doi: 10.3934/mbe.2015.12.83

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