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Persistence and global stability in a population model. (English) Zbl 0912.34040
A difference equation modelling the dynamics of a population undergoing a density-dependent harvesting is considered. A sufficient condition is established for all positive solutions to the corresponding discrete dynamic system to converge eventually to a positive equilibrium. Elementary methods of differential calculus are used. The result provides a generalization of a result known for a simpler special model with no harvesting.

34D05Asymptotic stability of ODE
92D25Population dynamics (general)
39A10Additive difference equations
Full Text: DOI
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