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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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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:
March 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:
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Distribution:
Open Access

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

References:

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