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A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

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Abstract:

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

Info:

Periodical:
The Bulletin of Society for Mathematical Services and Standards (Volume 1)
Pages:
21-32
DOI:
https://doi.org/10.18052/www.scipress.com/BSMaSS.1.21
Citation:
A.V. Papa Rao et al., "A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey", The Bulletin of Society for Mathematical Services and Standards, Vol. 1, pp. 21-32, 2012
Online since:
Mar 2012
Authors:
A.V. Papa Rao, K. Lakshmi Narayan, Shahnaz Bathul
Keywords:
Competitor, Equilibrium Points, Global Stability, Local Stability, Normal Steady State, Numerical Examples, Predator, Prey, Trajectories
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

ArchanaReddy. R; PattabhiRamacharyulu N. Ch &KrishnaGandhi.B., A stability analysis of two competitive interacting species with harvesting of both the species at a constant rate. International journal of scientific computing (1) January-June 2007: pp.57-68.

Freedman H. I., Deterministic Mathematical Models in Population Ecology, Decker, New York, (1980).

Kapur J.N., Mathematical Modeling in Biology and Medicine. Affiliated east west, (1985).

Kapur J.N., Mathematical modeling, wiley, easter, (1985).

Lakshmi Narayan K., and Pattabhiramacharyulu N. Ch. A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with a Gestation Period for Interaction, Int.J. Open Problems Compt. Math. Vol. 1, June 2008, 71-79.

Lakshmi Narayan K., & Pattabhiramacharyulu, N. CH A Prey - Predator Model with cover for Prey and an Alternative Food for the Predator and Constant Harvesting of Both the Species" Jordan Journal of Mathematics and Statistics, Vol 2(1), 2009, pp.43-45.

Shiva Reddy K. , Lakshmi Narayan K., and Pattabhiramacharyulu,N. Ch., A Three Species Eco system consisting of A Prey And Two Predators, International J. of Math. Sci. &Engg. Appls. Vol 4 No. IV(October, 2010), pp.129-145.

Shiva Reddy K., Lakshmi Narayan K., and Pattabhiramacharyulu,N. Ch., A Three Species Eco system consisting of A Prey, Predator and Super Predator,. International J. of Mathematics Applied in Science and Technology, Vol 2 , No. 1(2010), pp.95-107.

Ravindra Reddy. Lakshmi Narayan K., , Pattabhiramacharyulu.N. Ch, On Global Stability of Two Mutually Interacting Species With Limited Resources for Both the Species, Int. j. of Contemp. Math. Sciences, Vol. 6, 2011, No. 9, pp.401-407.

Ravindra Reddy, Lakshmi Narayan K., and others. A model of Two Mutually Interacting Species With Limited Resources for Both the Species, Int. J. of Engg. Re. Ind, App., Vol 2, No. II, pp.281-291.

Ravindra Reddy, Lakshmi Narayan K., Pattabhiramacharyulu.N. Ch, A model of Two Mutually Interacting Species With Limited Resources and Harvesting of Both the Species at a constant rate, Int. J. of Math. Sci. & Engg. Appls., Vol 4, No. III, (August2010). pp.97-106.

Shanker. N Lakshminarayan. K, Pattabhiramacharyulu.N. Ch. On the global Stability of a four Species: A Prey-Predator-Host-Commensal-Mutual-Syn Eco-System-II(Prey and Predator Washed Out States), , International J. of Math. Sci. & Engg. Appls. Vol 4 No. V (December, 2010), pp.409-427.

Paparao. A . V, Lakshmi. Narayan. K A prey -predator model with a cover linearly varying with the prey population and an alternative food for the predator, IJOPCM (vol2, No: 2, June 2009).

Paul Colinvaux, Ecology, John Wiley and Sons Inc., New York, (1977).

Lotka A.J., Elements of Physical Biology, Williams and Wilkins, Baltimore, New York, (1925).

Volterra V, Leçons sur la théorie mathématique de la lutte pour la vie, Gauthier-Villars, Paris, (1931).

T.K. kar, and K.S. chaudhuri , harvesting in two Prey one predator fishery : A Bionomic model. ANZIAMJ. 2004, 45 : 443-456.

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