Prey-Predator System; Having Stable Periodic Orbit

Authors

1 Department of Mathematics, University of Neyshabur, Neyshabur, Iran.

2 Department of Mathematics, University of Ilam, Ilam, Iran.

Abstract

The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.

Keywords


1. H.I. Freedman, Deterministic Mathematical Models in Population Ecology, 2nd ed., HIFR Consulting LTD, Edmonton, Canada (1987).

2. X.-C. Huang, S. J. Merrill, Conditions for uniqueness of limit cycles in general predatorprey systems, Math. Biosci. 96,(1989), 47-60.

3. Y. Kuang, H. I. Freedman, Uniqueness of Limit Cycles in Gause-Type Models of Predator Prey Systems, Math. Biosci. 88, (1988), 67-84.

4. M.H. Rahmani Doust, Di_erential Equations and Ecology, University of Neyshabur,

Neyshabur, (2013), 230-246.

5. M.H. Rahmani Doust, S. Gholizade, The Stability of Some systems of Harvested Lotka Volterra Predator-Prey Equations, Caspian Journal of Mathematical sciences, vol.3, No.1, (2014), 141-150.

6. M.H. Rahmani Doust, S. Gholizade, An Analysis of The Modi_ed Lotka-Volterra Predator-Prey Model, GMN, Article in press.

7. M.H. Rahmani Doust, S. Gholizade, The Lotka-Volterra Predator-Prey Equations, Caspian Journal of Mathematical sciences, vol.3, No.1, (2014), 227-231.