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Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Univ Agder, Dept Math Sci, N-4604 Kristiansand, Norway.
2013 (English)In: Journal of Applied Mathematics, ISSN 1110-757X, E-ISSN 1687-0042, 167671- p.Article in journal (Refereed) Published
Abstract [en]

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sanchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter sigma associated with the intensity of harvesting is explored. As sigma grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically.

Place, publisher, year, edition, pages
New York, USA: Hindawi Publishing Corporation, 2013. 167671- p.
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-70370DOI: 10.1155/2013/167671ISI: 000317211900001OAI: diva2:621324
Available from: 2013-05-14 Created: 2013-05-14 Last updated: 2013-05-14Bibliographically approved

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Rogovchenko, Yuriy V.
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