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A Mathematical Study of Two Species Commensalism Model
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In this present paper we discussed two species commensalism model. Here first species (x) is commensal and the second species (y) is host. Commensalism is Ecological model interaction between two organisms. One organism benefits from other without harmed by the organism. Here we governed two non linear differential equations with natural resources and the model is represented by coupled non linear ordinary differential equations. All the equilibrium points are identified and discussed the local stability in each stage and also discussed the global stability by constructing suitable Lyapunov function and supported by numerical simulations using Mat Lab.
Keywords
Commensal, Host, Equilibrium Point, Global Stability, Lyapunov Function.
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- Lakshmi Narayan. K.: A Mathematical study of Prey-Predator Ecological Models with a partial covers for the prey and alternative food for the predator, Ph.D thesis, 2004, J.N.T. University.
- Lakshmi Naryan. K., and Pattabhi Ramacharyulu. N.ch: Some threshold theorems for prey-predator model with harvesteng”, Int. J. of Math.Sci. and Engg. Appls, vol (2), No.2, 2008, PP-23-3.
- Lotka. A.J.: Elements of physical biology, Williams and Wilkins, Baltimore, 1925.
- Matsuda. H and Abrams .P.A.: Effects of predators-prey interaction and adaptive change on sustainable yield, Can. J. Fish. Aquat. Sci./J. Can. Sci. Halieut. Aquat., 61 (2004) 175-184.
- May, R.M.: Stability and complexity in model Eco-Systems”, Princeton University press, Princeton, 1973.
- Mesterton-Gibbons.M.: A technique for finding optimal two species harvesting policies, Ecol.model., 92 (1996) 235-244.
- Meyer, W.J.: Concepts of Mathematical Modeling, McGraw –Hill, 1985.
- Paul Colinvaux.: Ecology, John Wiley and Sons Inc., New York, 1986.
- Phanikumar. N., Pattabhiramacharyulu.N.Ch.,: “A three species eco-system consisting of a prey predator and host commensal to the prey” International journal of open problems compt.math, 3(1),(2010).92-113.
- Rish, S. and D.H. Boucher.: 1976 what ecologist looks for. Bulletin of the Ecological Society of America 57:8-9.
- Varma, V.S.: A note on Exact solutions for a Special prey-predator or competing Species System, Bull. Math. Biol. vol.39, 1977, PP 619-622.
- Volterra, V: Leconssen la theorie mathematique de la leitte pou lavie, Gauthier-Villars, Paris,1931.
- Sita Rambabu. B., Lakshmi Narayan. K., and Shahanaz Bathul.: A Mathematical study of Two Species Amensalism Model With a Cover for the first Species by Homotopy Analysis Method, Advances in Applied Science Research, 2012, 3 (3): pp: 1821-1826 Pelagia Research Library.
- A Two Species Amensalism Model 4with Harvesting By Homotopy Analysis Method”, B. Sita Rambabu, K. L. Narayan and Shahanaz Bathul, Bulletin of Society for mathematical services & standards (B SO MAS S),Vol. I No. 1 (2012), pp. 1-10.
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