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Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting


Citation

Toaha, Syamsuddin and Abu Hassan, Malik and Ismail, Fudziah and Leong, Wah June (2008) Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting. Malaysian Journal of Mathematical Sciences, 2 (2). pp. 147-159. ISSN 1823-8343; ESSN: 2289-750X

Abstract

In this paper we present a deterministic and continuous model for predator - prey population model based on Lotka-Volterra model. The model is then developed by considering time delay and the two populations are subjected to constant effort of harvesting. We study analytically the necessary conditions of harvesting to ensure the existence of the equilibrium points and their stabilities. The methods used to analyze the stability are linearization and by investigation the eigenvalues of the Jacobian matrix. The results show that there exists a globally asymptotically stable equilibrium point in the positive quadrant for the model with and without harvesting. The time delay can induce instability and a Hopf bifurcation can occur. The stable equilibrium point for the model with harvesting is then related to profit function problem. We found that there exists a critical value of the effort that maximizes the profit and the equilibrium point also remains stable. This means that the predator and prey populations can live in coexistence and give maximum profit although the two populations are harvested with constant effort of harvesting.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Publisher: Institute for Mathematical Research, Universiti Putra Malaysia
Keywords: Predator-prey; Time delay; Jacobian matrix; Eigenvalues; Effort of harvesting; Profit
Depositing User: Najwani Amir Sariffudin
Date Deposited: 18 Feb 2013 09:23
Last Modified: 01 Jun 2015 08:29
URI: http://psasir.upm.edu.my/id/eprint/16820
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