Influence of Non-Selective Harvesting and Prey Reserve Capacity on Prey-Predator Dynamics

 International Journal of Mathematical Trends and Technology (IJMTT) © 2013 by IJMTT Journal Volume-4 Issue-11 Year of Publication : 2013 Authors : Manju Agarwal , Rachana Pathak

Manju Agarwal , Rachana Pathak."Influence of Non-Selective Harvesting and Prey Reserve Capacity on Prey-Predator Dynamics"International Journal of Mathematical Trends and Technology (IJMTT),V4(11):295-309 2013. Published by Seventh Sense Research Group.

Abstract
In the present paper, we have developed a simple two species prey-predator model in which the prey dispersal in a two patch environment, one is assumed to be a free hunting zone and the other is a reserved zone where hunting and other extractive activities are prohibited. We assume that the prey possesses heterogeneous intrinsic growth rate with uniform carrying capacity. We also see the effect of non selective harvesting on prey-predator system in a free hunting zone. Criteria for local stability of the non-negative equilibria are obtained. Using differential inequality, we obtain sufficient conditions that ensure the persistence of the system. Finally, numerical simulations are given to verify the analytical results with the help of different sets of parameters.

References

[1]M. Agarwal and R. Pathak, “Role of Additional Food to Common Predator on Dynamics of Two Competing Preys”, International Journal of Applied Mathematics, Vol.28 (1), pp. 1145-1171, 2013.
[2]P. A. Braza, “A dominant predator and a prey’’, Math. Bio.Sci.and Engg. Vol. 5(1), pp. 61-73, 2008.
[3]M. Bandyopadhyay and J. Chattopadhyay, “Ratio-dependent predator-prey model: effect of environmental fluctuation and stability”. Nonlinearity, Vol. 18, pp. 913-936, 2005.
[4]C. W. Clark, Mathematical Bioeconomics: The optimal Management of Renewable Re-sources, 2nd ed., John Wiley and Sons, New York, 1990.
[5]B. Dubey, P. Chandra and P. Sinha, “A resource dependent fishery model with optimal harvestig policy”, J. Biol. Syst., Vol. 10, pp. 1-13, 2002.
[6]B. Dubey and R. K. Upadhyay, “Persistence and extinction of one prey and two predator system”, J. Nonlinear Anal. Appl: Model and Control, Vol. 9(4), pp. 307-329, 2004.

Keywords
Prey-Predator, Reserve Area, Harvesting, Stability, Persistence.