A study of prey-predator model with harvesting on susceptible prey and predator

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    In this paper, we study the prey predator model with susceptible prey and predator. Stability of the system is discussed in the present model. We analyzed the model in terms of catch rate coefficient.

  • Keywords

    Prey; Predator; Harvesting; SI Model; Equilibrium Point; Stability.

  • References

      [1] Brauer, F. and Soudack, A.C., Stability regions and transition phenomena for harvested predator-prey systems. J. Math. Biol. 7, (1979); 319-337. http://dx.doi.org/10.1007/BF00275152.

      [2] Brauer, F. and Soudack, A.C., Stability regions in predator-prey systems with constant-rate prey harvesting. J. Math. Biol. 8, (1979); 55-71. http://dx.doi.org/10.1007/BF00280586.

      [3] Brown, J. S. and Kotler, B. P., Hazardous duty pay and the foraging cost of predation. Ecology Letters 7, (2004); 999-1014.http://dx.doi.org/10.1111/j.1461-0248.2004.00661.x.

      [4] Chaudhuri, K.S. and Ray, S.S., on the combined harvesting of a prey-predator system, J. Biol. Sys. 4. (1996); 373-389. http://dx.doi.org/10.1142/S0218339096000259.

      [5] Clark, C.W., the Optimal Management of Renewable Resources. John Wiley ki Sons, MathemalicalBioeconomics, New York, (1979).

      [6] Creel, S. and Christanson, D., Relationships between direct predation and risk effects. Trends in Ecology and Evolution 23, (2008); 194-201.http://dx.doi.org/10.1016/j.tree.2007.12.004.

      [7] Dai, G. and Tang, M., Coexistence region and global dynamics of a harvested predator-prey system. SIAM J Appl. Math. 58, (1998); 193-210.http://dx.doi.org/10.1137/S0036139994275799.

      [8] Heithaus, M. R., Frid, A., Wirsing, A. J. and Worm, B., Predicting ecological consequences of marine top predator declines. Trends in Ecology & Evolution 23, (2008); 202-210.http://dx.doi.org/10.1016/j.tree.2008.01.003.

      [9] Leung, A., Optimal harvesting co-efficient control of steady state prey-predator diffusive Volterra-Lotka systems, Appl. Math. Optim. 31, (1995); 219.http://dx.doi.org/10.1007/BF01182789.

      [10] Levin, S.A., Hallam, T.G. and Gross, J.L., Applied Mathematical Ecology, Springer-Verlag, (1989).http://dx.doi.org/10.1007/978-3-642-61317-3.

      [11] Lima, S. L. and Dill, L. M., Behavioral decisions made under the risk of predation: a review and prospectus. Canadian Journal of Zoology 68, (1990); 619-640.http://dx.doi.org/10.1139/z90-092.

      [12] Lima, S. L., Stress and decision making under the risk of predation: recent developments from behavioral, reproductive, and ecological perspectives. Advances in the Study of Behavior 27, (1998); 215-290.http://dx.doi.org/10.1016/S0065-3454(08)60366-6.

      [13] Myerscough, M. R., Gray, B.E., Hograth, W.L. and Norbury, J., An analysis of an ordinary differential equation model for a two-species predator-prey system with harvesting and stocking, .I. Math. Bzol. 30. (1992); 389-411. http://dx.doi.org/10.1007/bf00173294.

      [14] Preisser, E., Bolnick, D. I. and Benard, M. F., Scared to death? The effects of intimidation and consumption in predator–prey interactions. Ecology 86, (2005); 501-509.http://dx.doi.org/10.1890/04-0719.

      [15] Schmitz, O., Krivan, V. and Ovadia, O., Trophic cascades: the primacy of trait-mediated indirect interactions. Ecology Letters 7, (2004); 153-163.http://dx.doi.org/10.1111/j.1461-0248.2003.00560.x.

      [16] Werner, E. E. and Peacor, S.D., A review of trait-mediated indirect interactions in ecological communities. Ecology 84, (2003); 1083-1100.http://dx.doi.org/10.1890/0012-9658(2003)084[1083:AROTII]2.0.CO;2.

      [17] Wuhaib, S. and A., Hasan, Y. A., A prey predator model with vulnerable infected prey. Applied Mathematical Sciences 6, 107, (2012); 5333-5348.




Article ID: 5856
DOI: 10.14419/gjma.v4i2.5856

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.