Cover Image

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

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 conditio...

Full description

Saved in:
Bibliographic Details
Main Authors: Toaha, Syamsuddin, Abu Hassan, Malik, Ismail, Fudziah, Leong, Wah June
Format: Article
Language:English
Published: Institute for Mathematical Research, Universiti Putra Malaysia 2008
Online Access:http://psasir.upm.edu.my/id/eprint/16820/1/16820.pdf
http://psasir.upm.edu.my/id/eprint/16820/
http://einspem.upm.edu.my/journal/volume2.2.php
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.16820
record_format eprints
spelling my.upm.eprints.168202015-06-01T08:29:54Z http://psasir.upm.edu.my/id/eprint/16820/ Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting Toaha, Syamsuddin Abu Hassan, Malik Ismail, Fudziah Leong, Wah June 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. Institute for Mathematical Research, Universiti Putra Malaysia 2008 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/16820/1/16820.pdf 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 http://einspem.upm.edu.my/journal/volume2.2.php
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description 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.
format Article
author Toaha, Syamsuddin
Abu Hassan, Malik
Ismail, Fudziah
Leong, Wah June
spellingShingle Toaha, Syamsuddin
Abu Hassan, Malik
Ismail, Fudziah
Leong, Wah June
Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting
author_facet Toaha, Syamsuddin
Abu Hassan, Malik
Ismail, Fudziah
Leong, Wah June
author_sort Toaha, Syamsuddin
title Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting
title_short Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting
title_full Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting
title_fullStr Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting
title_full_unstemmed Stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting
title_sort stability analysis and maximum profit of predator - prey population model with time delay and constant effort of harvesting
publisher Institute for Mathematical Research, Universiti Putra Malaysia
publishDate 2008
url http://psasir.upm.edu.my/id/eprint/16820/1/16820.pdf
http://psasir.upm.edu.my/id/eprint/16820/
http://einspem.upm.edu.my/journal/volume2.2.php
_version_ 1643826329136660480
score 13.250246

Similar Items