Generalize Prey-Predator Model with Reserve and Unreserved Area

Authors(3) :-Nayna Kadam, M. S. Chouhan, V. H. Badshah

In this paper we generalized a prey-predator model with prey dispersal in a two patch environment, one is assumed to be free zone and other is reserved zone where fishing and other extractive activities are prohibited. The steady states of the system are determined. The local and global stability analysis has been carried out.

Authors and Affiliations

Nayna Kadam
Asst. Prof. Chameli Devi Group of Institution, Indore, Madhya Pradesh, India
M. S. Chouhan
Asst. Prof. New Excellence, College, Bhopal, Madhya Pradesh, India
V. H. Badshah
Professor and Head, School of Studies in Mathematics, Ujjain, Madhya Pradesh, India

Stability, Equilibrium, Prey-Predator Model, Liapunov Function

  1. B. Dubey A Prey Predator Model with a Reserved Area, Nonlinear Analysis: Modelling and Control , Vol.-12,No.4, (2007), 478-494.
  2. B. Dubey, R. K. Upadhyay, Persistence and extinction of one prey and two predator system, J. Nonlinear Anal. Appl: Model and Control, 9(4), (2004), 307-329.
  3. B. Singh, B.K. Joshi, A. Sisodia, Effect of two interacting populations on resource following generalized logistic growth, Appl. Math. Sci., 5(9), (2011), 407-420.
  4. C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resourses, Wiley, New York,(1976).
  5. G. Birkoff , G.C. Rota, Ordinary Differential Equations, Ginn, 1982.
  6. H. Mehta ,B.Singh, N.Trivedi, R.Khandelwal”Prey-Predator Model with Reserved and Unreserved Area Having Modified Transmission Function” Pelagia Research Library, 3(4),(2012),1978-1985
  7. J. B. Collings, Bifurcation and stability analysis of a temperature dependent mite predator-prey interaction model incorporating a prey refuge, Bull. Math. Biol., 57(1), 63–76, 1995.
  8. J. La Salle, S. Lefschetz, Stability by Liapunov’s Direct Method with Applications, AcademicPress, New York, London, 1961.
  9. T.K Kar ,”Selective Harvesting in a Prey Predator Fishery with Time Delay”, Mathematical and Computer Modelling 38,(2003), 449-458.
  10. T.K.Kar, M. Swarnakamal, Influence of prey reserve in a prey-predator fishery, Nonlinear Analysis,65(2006),1725-1735.
  11. X. Zhang, L. Chen , A.U. Neumann “The Stage Structured Predator –Prey Model and Optimal Harvesting Policy”, Mathematical Bio. Sci.168, (2000), 201-210.

Publication Details

Published in : Volume 1 | Issue 5 | September-October 2015
Date of Publication : 2015-10-25
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 295-298
Manuscript Number : IJSRSET151548
Publisher : Technoscience Academy

Print ISSN : 2395-1990, Online ISSN : 2394-4099

Cite This Article :

Nayna Kadam, M. S. Chouhan, V. H. Badshah, " Generalize Prey-Predator Model with Reserve and Unreserved Area, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 1, Issue 5, pp.295-298, September-October-2015.
Journal URL :

Article Preview