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Journal of Mathematics
Volume 2013, Article ID 613706, 9 pages
http://dx.doi.org/10.1155/2013/613706
Research Article

A Mathematical Model for Optimal Management and Utilization of a Renewable Resource by Population

Department of Mathematics, Birla Institute of Technology & Science, Pilani 333031, India

Received 20 August 2012; Accepted 20 October 2012

Academic Editor: Kaleem R. Kazmi

Copyright © 2013 B. Dubey and Atasi Patra. 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.

Abstract

A dynamical model is proposed and analyzed to study the effect of the population on the resource biomass by taking into account the crowding effect. Biological and bionomical equilibria of the system are discussed. The global stability behavior of the positive equilibrium is studied via the output feedback control. An appropriate Hamiltonian function is formed for the discussion of optimal harvesting of resource which is utilized by the population using Pontryagin's Maximum Principal. A numerical simulation is performed on the model to analyze the theoretical results.