A Three Species Ecological Model with a Predator and Two Preying Species

Vidyanath, Tripuraribhatla; Narayan, K. Lakshmi; Bathul, Shahnaz

doi:10.18052/www.scipress.com/IFSL.9.26

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A Three Species Ecological Model with a Predator and Two Preying Species

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Abstract:

The present paper is devoted to an analytical study of a three species ecological model in which a predator is preying on the other two species which are mutually helping each other. In addition to that, all the three species are provided with an alternate food. The model is characterized by a set of first order non-linear differential equations. All the possible equilibrium points of the model have been derived and the local and global stability for the positive equilibrium point is discussed and supported by the numerical simulation using the MATLAB.

Info:

Periodical:

International Frontier Science Letters (Volume 9)

Pages:

26-32

DOI:

https://doi.org/10.18052/www.scipress.com/IFSL.9.26

Citation:

T. Vidyanath et al., "A Three Species Ecological Model with a Predator and Two Preying Species", International Frontier Science Letters, Vol. 9, pp. 26-32, 2016

Online since:

August 2016

Authors:

Tripuraribhatla Vidyanath, K. Lakshmi Narayan, Shahnaz Bathul

Keywords:

Global Stability, Local Stability, Mutualism, Predator, Prey

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Open Access

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Creative Commons Attribution 4.0 International License

References:

[1] T. H. Fay, J. C. Greeff, Testing the model for one predator and two mutualistic prey species, Elsevier, Ecological modeling. 196 (2006) 245-255.

[2] J.M. Cushing, Integro-differential equations and Delay models in Population Dynamics, Lecture Notes in Biomathematics, Springer-Verlag, Heidelberg, 20 (1997).

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

[4] A.J. Lotka, Elements of Physical biology, Williams and Wilkins, Baltimore, (1925).

[5] W.J. Meyer, Concepts of Mathematical Modelling, Mc Graw-Hill, (1985).

[6] V. Volterra, Leconssen la Theorie Mathematique de la Leitte Pou Lavie. Gauthier-Villars, Paris, (1931).

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

[8] A.V. Paparao, K. Lakshmi Narayan, Shahnaz Bathul, A three species ecological model with a prey, predator and competitor to the prey and optimal harvesting of the prey, Journal of Advanced Research in Dynamical and control systems. 5 (2013) 37-49.

[9] T. Vidyanath, K. Lakshmi Narayan, Shahnaz Bathul, A three species synecological model with mutualism, neutralism and prey-predation, Proceedings NCPAM, VIT, Chennai. (2014) 60-64.

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