Model for the Dynamical Study of a Three-Species Food-Chain System under Toxicant Stress

Authors(4) :-Raveendra Babu. A , O. P. Misra, Chhatrapal Singh, Preety Kalra

The modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system and the state variables of the models are prey and predator densities, concentration of toxicant in the environment and the concentration of toxicant in the prey population. In the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. The stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the stress of toxicant are obtained. Further, it is also found that the predation rate of the intermediate predator is a bifurcating parameter and Hopf-bifurcation occurs at some critical value of this parameter. Finally, numerical simulation is carried out to support the analytical results.

Authors and Affiliations

Raveendra Babu. A
School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, India
O. P. Misra
School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, India
Chhatrapal Singh
School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, India
Preety Kalra
School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, India

Stability, Bifurcation, Lyapunov function.

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Publication Details

Published in : Volume 1 | Issue 2 | March-April 2015
Date of Publication : 2015-04-25
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 493-513
Manuscript Number : IJSRSET1522134
Publisher : Technoscience Academy

Print ISSN : 2395-1990, Online ISSN : 2394-4099

Cite This Article :

Raveendra Babu. A , O. P. Misra, Chhatrapal Singh, Preety Kalra, " Model for the Dynamical Study of a Three-Species Food-Chain System under Toxicant Stress, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 1, Issue 2, pp.493-513, March-April-2015. Citation Detection and Elimination     |     
Journal URL : https://ijsrset.com/IJSRSET1522134

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