PERIODIC SOLUTIONS FOR A DIFFERENTIAL EQUATION OF A RENEWABLE RESOURCE SUBJECT TO ADDITIVE ALLEE EFFECTS

Article Sidebar

PDF
Published: Apr 26, 2015

Main Article Content

Birku Demewoz Misganaw
University of Gondar

Abstract

Allee effect refers to reduction of individual fitness at low population densities. In this article we establish existence of positive periodic solutions for a model representing dynamics of a renewable resource which is subject to additive Allee effect. A fixed point theorem in cones has been employed to establish the existence of the periodic solutions.

Downloads

Download data is not yet available.

Article Details

How to Cite
Misganaw, B. D. (2015). PERIODIC SOLUTIONS FOR A DIFFERENTIAL EQUATION OF A RENEWABLE RESOURCE SUBJECT TO ADDITIVE ALLEE EFFECTS. Journal of Global Research in Mathematical Archives(JGRMA), 2(7), 23–31. Retrieved from https://www.jgrma.com/index.php/jgrma/article/view/216
Issue
Vol. 2 No. 7 (2014): July-2014
Section
Research Paper

Open Access: This is an open-access journal. All articles published in the Journal of Global Research in Mathematical Archives(JGRMA) are made immediately and permanently available under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. Authors retain the copyright of their work and grant Journal of Global Research in Mathematical Archives(JGRMA)  the right of first publication. This license permits unrestricted use, distribution, adaptation, and reproduction in any medium or format, including commercial use, provided the original author(s), source, and license are properly acknowledged.

Google Scholar Indexed | DOI Enabled | OAI-PMH Compliant | Open Access Journal

Author Biography

Birku Demewoz Misganaw, University of Gondar

University of Gondar

College of Natural and Computational Sciences

Department of Mathematics

References

P. Aguirre, E. G. Olivares and E. Saez, Two limit cycles in a Leslie-

Gower predator-prey model with additive Allee eect, Nonlinear Anal-

ysis: Real World Applications 10(2009)1401 - 1416.

P. Aguirre, E.G. Olivares and E. Saez, Three limit cycles in a Leslie-

Gower predator- prey model with additive Allee eect. Siam J. Appl.

Math., 69(5)(2009)12441262.

W.C. Allee, Animal aggregations, University of Chicago Press, Chicage, IL, 1931.

W.C. Allee, Cooperation among animals, Henry Schuman, New York,

L. Berec, E. Angulo and F. Counchamp, Multiple Allee eects and pop-

ulation management. TREE 22(4)(2006) 185-191.

D. S. Boukal and L. Berec, Single-species models of the Allee ef-

fect:extinction boundaries, sex ratios and mate encounters. J. theor.Biol.

(2002) 375-394. environment, Math. Biosc. 205(2007) 1-18.

C. W. Clark, Mathematical Bioeconomic: The optimal management of

renewable resources, (second edition). John Wiley and Sons, 1990.

F. Courchamp, T. C. Brock and B. Grenfell, Inverse dependence and

the Alle eect, TREE 14(10)(1999) 405-410.

F. Courchamp, L. Berec and J. Gascoigne, Allee Eects in Ecology and

Conservation, Oxford University Press, Oxford, 2008.

B. Dennis and G. P. Patil, The gamma distribution and weighted multi-model gamma distributions as models of population abundance. Math.Biosci. 68(1984) 187-212.

B. Dennis, Allee eects: population growth, critical density, and the

chance of extinction, Natural Resource Modeling 3(4)(1989) 481-538.