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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

On the Dynamics of a General Predator-Prey System

M. M.A. El-Sheikh, S. A.A. El-Marouf and Z. M. Alaofy

Abstract

Problem statement: In this study a general two dimensional predator-prey model is considered. The dynamic and existence of equilibrium points are studied. Conclusion/Recommendations: Hopf bifurcation is discussed. The existence and uniqueness of limit cycles is proved. Special cases are considered to justify our results.

Journal of Mathematics and Statistics
Volume 7 No. 4, 2011, 295-301

DOI: https://doi.org/10.3844/jmssp.2011.295.301

Submitted On: 25 September 2011 Published On: 28 October 2011

How to Cite: El-Sheikh, M. M., El-Marouf, S. A. & Alaofy, Z. M. (2011). On the Dynamics of a General Predator-Prey System. Journal of Mathematics and Statistics, 7(4), 295-301. https://doi.org/10.3844/jmssp.2011.295.301

Open AccessCopyright: © 2011 M. M.A. El-Sheikh, S. A.A. El-Marouf and Z. M. Alaofy. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Predator-prey system
  • functional response
  • limit cycles
  • hopf bifurcation
  • mathematics subject classification
  • analyzing models
  • interacting species
  • predator population
  • efficiency rate