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


Affiliations
1 Dept. of Mathematics, AVNIET, Hyderabad, India
2 Dept. of Mathematics, VITS, Hyderabad, India
3 Dept. of Mathematics, JNTUH, Hyderabad, India
     

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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.

Keywords

Prey-Predation, Routh-Hurwitz Criterion, Global Stability, Stochastic Process.
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  • Deterministic and Stochastic Stability Analysis of a Three Species Eco-System with a Predator and Two Preys

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Authors

T. Vidyanath
Dept. of Mathematics, AVNIET, Hyderabad, India
K. Lakshmi Narayana
Dept. of Mathematics, VITS, Hyderabad, India
Shahnaz Bathul
Dept. of Mathematics, JNTUH, Hyderabad, India

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.

Keywords


Prey-Predation, Routh-Hurwitz Criterion, Global Stability, Stochastic Process.

References