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

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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