Abstract and Applied Analysis

The Stability of Gauss Model Having One-Prey and Two-Predators

A. Farajzadeh, M. H. Rahmani Doust, F. Haghighifar, and D. Baleanu

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Abstract

The study of the dynamics of predator-prey interactions can be recognized as a major issue in mathematical biology. In the present paper, some Gauss predator-prey models in which three ecologically interacting species have been considered and the behavior of their solutions in the stability aspect have been investigated. The main aim of this paper is to consider the local and global stability properties of the equilibrium points for represented systems. Finally, stability of some examples of Gauss model with one prey and two predators is discussed.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 219640, 9 pages.

Dates
First available in Project Euclid: 15 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1329337688

Digital Object Identifier
doi:10.1155/2012/219640

Mathematical Reviews number (MathSciNet)
MR2872297

Zentralblatt MATH identifier
1234.34034

Citation

Farajzadeh, A.; Doust, M. H. Rahmani; Haghighifar, F.; Baleanu, D. The Stability of Gauss Model Having One-Prey and Two-Predators. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 219640, 9 pages. doi:10.1155/2012/219640. https://projecteuclid.org/euclid.aaa/1329337688


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References

  • T. A. Burton, Volterra Integral and Differential Equations, vol. 167, Academic Press, Orlando, Fla, USA, 1983.
  • E. M. Elabbasy and S. H. Saker, “Dynamics of a class of non-autonomous systems of two non-interacting preys with common predator,” Journal of Applied Mathematics & Computing, vol. 17, no. 1-2, pp. 195–215, 2005.
  • S. Gakkhar and B. Singh, “The dynamics of a food web consisting of two preys and a harvesting predator,” Chaos, Solitons and Fractals, vol. 34, no. 4, pp. 1346–1356, 2007.
  • T. K. Kar and K. S. Chaudhuri, “Harvesting in a two-prey one-predator fishery: a bioeconomic model,” The Australian & New Zealand Industrial and Applied Mathematics Journal, vol. 45, no. 3, pp. 443–456, 2004.
  • S. Kumar, S. K. Srivastava, and P. Chingakham, “Hopf bifurcation and stability analysis in a harvested one-predator–-two-prey model,” Applied Mathematics and Computation, vol. 129, no. 1, pp. 107–118, 2002.
  • B. Lisena, “Asymptotic behaviour in periodic three species predator-prey systems,” Annali di Matematica Pura ed Applicata, vol. 186, no. 1, pp. 85–98, 2007.
  • G. P. Samanta, D. Manna, and A. Maiti, “Bioeconomic modelling of a three-species fishery with switching effect,” Journal of Applied Mathematics & Computing, vol. 12, no. 1-2, pp. 219–231, 2003.
  • X. Song and Y. Li, “Dynamic complexities of a Holling II two-prey one-predator system with impulsive effect,” Chaos, Solitons and Fractals, vol. 33, no. 2, pp. 463–478, 2007.