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Sita Rambabu, B.
- A Mathematical Study of Two Species Commensalism Model
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Authors
Affiliations
1 Vidya Jyothi Institute of Technology, Hyderabad, IN
1 Vidya Jyothi Institute of Technology, Hyderabad, IN
Source
Research Journal of Science and Technology, Vol 9, No 3 (2017), Pagination: 385-391Abstract
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.
References
- 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.
- A Two Species Amensalism Model with a Linearly Varying Cover on the First Species
Abstract Views :440 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, VJIT, Hyderabad-500085, IN
2 Department of Mathematics, VITS, Hyderabad - 508284, IN
1 Department of Mathematics, VJIT, Hyderabad-500085, IN
2 Department of Mathematics, VITS, Hyderabad - 508284, IN
Source
Research Journal of Science and Technology, Vol 9, No 4 (2017), Pagination: 511-520Abstract
The present paper is devoted to an analytical investigation of a two species ammensalism model with a cover linearly varying with the population on the first species (x) to protect from the attacks of the second species (y).All the equilibrium points are identified and the local stability is discussed and global stability is also discussed by constructing suitable Lyapunov’s function supported by the numerical simulation by using Matlab.Keywords
Ammensal, Cover, Equilibrium Point, Global Stability, Lyapunov Function.References
- 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. JNTUH.
- Lakshmi Naryan K, and Pattabhi Ramacharyulu NCh. Some threshold theorems for prey-predator model with harvesting. Int. J. of Math.Sci. and Engg. Appls 2008; 2: 23-3.
- Leonardo of Pisa (Fibonacci). Liberabaci (Book of counting board), 1202.
- Lotka. AJ. Elements of physical biology, Williams and Wilkins, Baltimore, 1925.
- Lucas WF Roberts SF and Thrall RM. Discreate and system models (vol (III) of modules in Applied Mathematics). Springer-verlag, Heidel berg, 1983.
- Marchuk GI. Mathematical Models in immunology. optimization software Inc., New York, 1983.
- Matsuda H and Abrams PA. Effects of predators-prey interaction and adaptive change on sustainable yield. Can. J. Fish. Aquat. Sci./J. Can. Sci. Halieut. Aquat. 2004; 61: 175-184.
- May RM. 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. 1996; 92: 235-244.
- Meyer WJ. Concepts of Mathematical Modeling. McGraw –Hill, 1985.
- Paul Colinvaux. Ecology. John Wiley and Sons Inc., New York, 1986.
- Phanikumar N, Pattabhiramacharyulu NCh. A three species eco-system consisting of a prey predator and host commensal to the prey. International Journal of Open Problems Compt. Math, 2010; 3(1): 92-113.
- Rish S and Boucher DH. 1976 what ecologist looks for. Bulletin of the Ecological Society of America 57: 8-9.
- Varma VS. A note on Exact solutions for a Special prey-predator or competing Species System. Bull.Math.Biol. 1977; 39: 619-622.
- Volterra V. Leconssen la Theorie Mathematique de la Leitte Pou Lavie. Gauthier-Villars, Paris,1931.
- Liao SJ. beyond perturbation: introduction to the homotopy analysis method.CRC Press. Boca Raton: Chapman & Hall. 2003.
- 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. Pelagia Research Library. 2012; 3 (3): 1821-1826.