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Research Journal of Science and Technology
Year : 2017, Volume : 9, Issue : 4
First page : ( 541) Last page : ( 548)
Print ISSN : 0975-4393. Online ISSN : 2349-2988.
Article DOI : 10.5958/2349-2988.2017.00093.6

Deterministic and Stochastic Stability Analysis of a Three Species Eco-System with a Predator and Two Preys

Vidyanath T1,*, Narayana Lakshmi K2, Bathul Shahnaz3

1Dept. of Mathematics, AVNIET, Hyderabad, India

2Dept. of Mathematics, VITS, Hyderabad, India

3Dept. of Mathematics, JNTUH, Hyderabad, India

*Corresponding author E-mail: vidyanath.t@gmail.com

Online published on 12 June, 2018.

Abstract

In this paper, we study a three species eco-system with a predator and two preys. Employing suitable techniques like Routh-Hurwitz criterion and Lyapunov, the local and global stability at the interior equilibrium point is analyzed. Also using Weiner process, the stochastic model corresponding to the deterministic model is constructed and it's exponential and mean square stability at the trivial solution is derived. Finally numerical simulations authenticate the existence of the system.

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Keywords

Prey-predation, Routh-Hurwitz criterion, Global Stability, Stochastic process.

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