doi: 10.7763/IJAPM.2012.V2.81
Harvesting in a Periodic Habitat with Allee Effect
Fatma Bayramoğlu Rizaner
,
- Eastern Mediterranean University, Dep. of Mathematics, Famagusta, TRNC, Mersin 10, Turkey
Abstract
The dynamics of a harvested single species that goes extinct when rare is described by a nonlinear differential equation &where <i>r</i>, <i>K</i>, <i>A</i> and h are positive continuous T-periodic functions. <i>N</i> is the population size, <i>A</i> (<i>0</i> < <i>A</i> < <i>K</i>) is the threshold population size below which <i>N</i> < 0 due to Allee effect, <i>r</i> is the intrinsic growth rate and <i>K</i> is the carrying capacity of the environment and <i>h</i> is the harvesting. The aim of this paper is to study the existence of periodic solutions and their stability properties. We discuss the effect of harvesting on a single species population in a fluctuating environment whose dynamics is described by a nonlinear differential equation.
Keywords
- Nonlinear
- differential
- equation;
- Allee
- Effect;
- periodic
- solutions;
- stability;
- existence;
- harvesting;
- positive
- solutions
How to Cite
Fatma Bayramoğlu Rizaner and Svitlana P. Rogovchenko, "Harvesting in a Periodic Habitat with Allee Effect," International Journal of Applied Physics and Mathematics, vol. 2, no. 3, pp. 175-178, 2012. https://doi.org/ 10.7763/IJAPM.2012.V2.81
Copyright & License
Copyright © 2012 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).