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


Raveendra Babu. A , O. P. Misra, Chhatrapal Singh, Preety Kalra
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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.

Raveendra Babu. A , O. P. Misra, Chhatrapal Singh, Preety Kalra

Stability, Bifurcation, Lyapunov function.

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Publication Details

Published in : Volume 1 | Issue 2 | March-April - 2015
Date of Publication Print ISSN Online ISSN
2015-04-25 2395-1990 2394-4099
Page(s) Manuscript Number   Publisher
493-513 IJSRSET1522134   Technoscience Academy

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.
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