A Mathematical Model for Optimal Management and Utilization of a Renewable Resource by Population. (17th January 2013)

• Record Type: Journal Article
• Authors: Dubey, B.; Patra, Atasi
• Other Names: Kazmi Kaleem R. Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2013(2013)
• Publication Date: 2013-01-17
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2013/613706
• Languages: English
• ISSNs: 2314-4629

Abstract

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.