Author, Subjects, Keywords

Cited Author

 
 
   » By Author or Editor
 » Browse Author by Alphabet
 » By Journal
 » By Subjects
 » Malaysian Journals
 » By Type
 » By Year
 » By Latest Additions
 
 
   » By Author
 » Top 20 Authors
 » Top 20 Article
 » Top Journal Cited
 » Top Article Cited
 » Journal Citation Statistics
 » Usage Since Sept 2007


 
 
 

Login | Create Account

Stability Analysis and Maximum Profit of One Prey-Two Predators Model under Constant Effort of Harvesting

Touha, Syamsuddin, and Malik Hj. Abu Hassan, and Fudziah Ismail, and Leong, Wah June, (2007) Stability Analysis and Maximum Profit of One Prey-Two Predators Model under Constant Effort of Harvesting. Malaysian Journal of Science, 26 (SKSM14 Special Issue). pp. 43-51. ISSN 13943065

Full text not available from this repository.

Official URL: http://www.ejum.fsktm.um.edu.my/

Affiliations

Hasanuddin University, Indonesia. Dept. of Mathematics.
Universiti Putra Malaysia. Dept. of Mathematics

Abstract

In this paper we present a deterministic and continuous model for one prey-two predators population model based on the Lotka-Volterra model. The two predators are subjected to constant effort of harvesting. We study analytically the necessary conditions of harvesting to ensure existence of the equilibrium points and their stabilities. The methods used to analyse the stability are linearisation and Hurwitz stability test. The results show that there is an asymptotically stable equilibrium point in positive octane for the model without constant effort of harvesting. We found that there is an asymptotically stable equilibrium point in positive octane for the model with constant effort of harvesting. The stable equilibrium point for the model with constant effort of harvesting is then related to profit function which we found to have maximum profit. This means that the prey and predator populations can live in coexistence and give maximum profit although the two predators are harvested with constant effort of harvesting.

Item Type:Journal
Keywords:Prey-predator, Hurwitz Stability Test, harvesting, profit
Subjects:Q Science, Computer Science
ID Code:2651

1. Takeuchi, Y. and Adachi, N. (1986). Dynamics and stability of ecological models. Ecological Modelling 32: 95-104.

2. Freedman, H. I. (1989). Persistence and extinction in model of two-habitat migration. Math. Comput. Modelling 12 (1): 105-112.

3. Ebenhoh, W. (1994). Competition and coexistence: Modelling approaches. Ecological Modelling 75/76: 83-98.

4. Cale, W.G. and O'Neill, R.Y. (1988). Aggregation and consistency problems in theoretical models of exploitative resource competition. Ecological Modelling 40: 97-109.

5. Rinaldi, S. and Muratori, S. (1992). Slow-fast limit cycles in predator-prey models. Ecological Modelling 61: 287-308.

6. Farkas, M. and Freedman, H. I. (1989). Stability conditions for two predator one prey systems. Acta Applicandae Mathematicae 14: 3-10.

7. Kuang, Y. and Takeuchi, Y. (1994). Predator-prey dynamics models of prey dispersal in two-patch environments. Math. Biosci. 120: 77-98.

8. Liu, Z. J. and Wang, W. D. (2004). Persistence and periodic solutions of a non autonomous predator-prey diffusion system with Holling III functional response and continuous delay. Discrete and Continuous Dynamical Systems Series B 4 (3): 653-662.

9. Jeffries, C. (1974). Qualitative stability and digraphs in model ecosystems. Ecology 55: 1415-1419.

10. Jeffries, C. (1989). Mathematical Model in Ecology, Boston: Birkhauser.

11. Willems, J. L. (1970). Stability Theory of Dynamical System. London: Thomas Nelson & Sons.

12. Clark, C. W. (1976). Mathematical Bioeconomics: The Optimal Management of Renewable Resources, New York: John Wiley & Sons.

Repository Staff Only: item control page
 
 
 
 
 
 
© Copyright 2007 MyAIS Faculty of Computer Science and Information Technology, University of Malaya – All Rights Reserved. Malaysian Abstracting and Indexing System is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton. More information and software credits.