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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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  • Lotka AJ. Elements of Physical biology. Williams and Wilkins, Baltimore, 1925.

  • Volterra V. Leconssen la Theorie Mathematique de la Leitte Pou Lavie. Gauthier-Villars,Paris, 1931.

  • Freedman HI. Deterministic Mathematical Models in Population Ecology. Marces Decker, New York, 1980.

  • Kapur JN. Mathematical Modeling in Biology and Medicine. Affiliated east-west, 1985.

  • Meyer WJ. Concepts of Mathematical Modelling. Mc Graw-Hill, 1985.

  • Cushing JM. Integro-differential equations and Delay models in Population Dynamics, Lecture Notes in Biomathematics. Springer- Verlag, Heidelberg, 20: 1997.

  • Murray JD. Models for interacting populations. Chapter 3, pp. 79-118.

  • Vidyanath T, Laxmi Narayan K, Shahnaz Bathul. A three species ecological model with a predator and two preying species. International Frontier Sciences Letters. 2016; 9: 26-32.

  • Ranjith Kumar G, Laxmi Narayan K, Ravindra Reddy B. Dynamics of an SIR epidemic model with a saturated incidence rate under stochastic influence. Global Journal of Pure and Applied Mathematics. 2015; 11(2): 175-179.

  • Gikhaman II, Skorokhod AV. The theory of stochastic process. Springer, 3rd ed: Berlin, 1979.

  • Afanasev VN, Kolmanowski VB, and Nosov VR. Mathematical Theory of Control System Design. Kluwer Academic, Dordrecht, Netherlands, 1996.


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

Abstract Views: 406  |  PDF Views: 1

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