INFORMATION CHANGE THE WORLD

International Journal of Modern Education and Computer Science (IJMECS)

ISSN: 2075-0161 (Print), ISSN: 2075-017X (Online)

Published By: MECS Press

IJMECS Vol.4, No.8, Aug. 2012

Discrete Model of Commensalism Between Two Species

Full Text (PDF, 364KB), PP.40-46


Views:171   Downloads:3

Author(s)

B. Hari Prasad,N. Ch. Pattabhi Ramacharyulu

Index Terms

Characteristic matrix,Commensal,Stable,Equilibrium point,Host

Abstract

This paper deals with an investigation on discrete model of host commensal pair. The model comprises of a commensal (S1), a host (S2) that benefit S1, without getting effected either positively or adversely. The model is characterized by a couple of first order non-linear ordinary differential equations. In all, four equilibrium points of the model would exist and their stability criteria is discussed. The model would be stable if each of the eigen values is numerically less than one. Further the growth rates of the species are numerically estimated using Runge-Kutta fourth order scheme.

Cite This Paper

B. Hari Prasad,N. Ch. Pattabhi Ramacharyulu,"Discrete Model of Commensalism Between Two Species", IJMECS, vol.4, no.8, pp.40-46, 2012.

Reference

[1]Lotka A. J., Elements of Physical Biology, Williams & Wilking, Baltimore, (1925).

[2]Volterra V., Leconssen La Theorie Mathematique De La Leitte Pou Lavie, Gauthier-Villars, Paris, (1931).

[3]May,R.M. Stability and Complexity in Model Eco-systems, Princeton University Pres, Princeton, 1973.

[4]Kushing J.M., Integro-Differential Equations and Delay Models in Population Dynamics, Lecture Notes in Bio-Mathematics, Springer Verlag, 20, (1977).

[5]Smith,J.M. Models in Ecology, Cambridge University Press, Cambridge, 1974.

[6]Kapur J. N., Mathematical Modelling in Biology and Medicine, Affiliated East West, (1985). 

[7]Srinivas N. C., "Some Mathematical Aspects of Modeling in Bio-medical Sciences" Ph.D Thesis, Kakatiya University, (1991).

[8]Lakshmi Narayan K. & Pattabhiramacharyulu. N. Ch., "A Prey-Predator Model with Cover for Prey and Alternate Food for the Predator and Time Delay," International Journal of Scientific Computing. 1, (2007), 7-14.

[9]Archana Reddy R., "On the Stability of some Mathematical Models in Biosciences- Interacting Species ", Ph.D.,Thesis, J.N.T.U, (2010).

[10]Bhaskara Rama Sharma B., "Some Mathematical Models in Competitive Eco-systems", Ph.D.,Thesis, Dravidian University,(2010).

[11]Phani Kumar N, "Some Mathematical Models of Ecological Commensalism", Ph.D., Thesis, A.N.U. (2010).

[12]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species : A Prey-Predator-Host-Commensal-Syn Eco-System-II" (Prey and Predator washed out states) "International eJournal of Mathematics & Engineering", 5, (2010), 60 – 74

[13]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species : A Prey-Predator-Host-Commensal-Syn Eco-System-VII" (Host of the Prey Washed Out States,) "International Journal of Applied Mathematical Analysis and Applications, Vol.6, No.1-2, Jan-Dec.2011, pp.85 - 94.

[14]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species : A Prey-Predator-Host-Commensal-Syn Eco-System-VIII" (Host of the Predator Washed Out States) "Advances in Applied Science, Research, 2011, 2(5), pp.197-206.

[15]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-I (Fully Washed Out State)", Global Journal of Mathematical Sciences : Theory and Practical, Vol.2, No.1, Dec.2010, pp.65 - 73.

[16]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-V (Predator Washed Out States)", Int. J. Open Problems Compt. Math. Vol.4, No.3, Sep.2011, pp.129 - 145.

[17]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-VII (Host of S2 Washed Out States)", Journal of Communication and Computer,Vol.8,No.6,June-2011,pp.415-421

[18]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-IV", Int. Journal of Applied Mathematics and Mechanics, Vol.8, Issue 2, 2012, pp.12 - 31.

[19]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-VIII", ARPN Journal of Engineering and Applied Sciences, Vol.7, Issue 2, Feb.2012, pp.235 - 242.

[20]Hari Prasad.B and Pattabhi Ramacharyulu. N.Ch., "On the Stability of a Four Species : A Prey-Predator-Host-Commensal-Syn Eco-System-IV" "International eJournal of Mathematics & Engineering", 29, (2010), pp. 277 - 292.