International Journal of Modern Education and Computer Science (IJMECS)
ISSN: 2075-0161 (Print), ISSN: 2075-017X (Online)
Published By: MECS Press
IJMECS Vol.6, No.11, Nov. 2014
A Study on Discrete Model of Three Species Syn-Eco-System with Limited Resources — (One Period Equilibrium States)
Full Text (PDF, 385KB), PP.38-44
In this paper, the system comprises of a commensal (S1), two hosts S2 and S3 ie., S2 and S3 both benefit S1, without getting themselves effected either positively or adversely. Further S2 is a commensal of S3, S3 is a host of both S1, S2 and all the three species have limited resources. The basic equations for this model constitute as three first order non-linear ordinary difference equations. All possible equilibrium points are identified based on the model equations and criteria for their stability are discussed. Further the numerical solutions are computed for specific values of the various parameters and the initial conditions.
Cite This Paper
B. Hari Prasad,"A Study on Discrete Model of Three Species Syn-Eco-System with Limited Resources — (One Period Equilibrium States)", IJMECS, vol.6, no.11, pp.38-44, 2014.DOI: 10.5815/ijmecs.2014.11.05
A.J. Lotka, "Elements of Physical Biology", Williams and Wilking, Baltimore, 1925.
V. Volterra, "Leconssen La Theorie Mathematique De La Leitte Pou Lavie", Gauthier-Villars, Paris, 1931.
A.P. Colinvaux, "Ecology", John Wiley, New York, 1986.
J.N. Kapur, "Mathematical Modeling in Biology and Medicine", Affiliated East West, 1985.
J.M. Kushing, "Integro-Differential Equations and Delay Models in Population Dynamics", Lecture Notes in Bio-Mathematics, Springer Verlag, 20, 1977.
W.J. Meyer, "Concepts of Mathematical Modeling", Mc.Grawhill, 1985.
N.C. Srinivas, "Some Mathematical Aspects of Modeling in Bio-medical Sciences", Kakatiya University, Ph.D Thesis, 1991.
K.L. Narayan and N.Ch.P.R. Charyulu, "A Prey-Predator Model with Cover for Prey and Alternate Food for the Predator and Time Delay", Int. J. of Scientific Computing, vol. 1, pp. 7 – 14, 2007.
R.A. Reddy, N.Ch.P.R. Charyulu and B.K. Gandhi, "A Stability Analysis of Two Competetive Interacting Species with Harvesting of Both the Species at a Constant Rate", Int. J. of Scientific Computing, vol. 1, pp. 57 – 68, 2007.
B. B. Rama Sharma and N.Ch. P.R. Charyulu, "Stability Analysis of Two Species Competitive Eco-system, Int. Journal of Logic Based Intelligent Systems, vol. 2, 2008.
R.R. Reddy, "A Study on Mathematical Models of Ecological Mutualism between Two Interacting Species", Osmania University, Ph.D. Thesis, 2008.
K.V.L.N. Acharyulu and N.Ch.P.R. Charyulu, "An Enemy- Ammensal Species Pair With Limited Resources –A Numerical Study", Int. J. Open Problems Compt. Math., vol. 3, pp. 339– 356, 2010.
K. V. L. N. Acharyulu and N. Ch. P. R. Charyulu, "An Ammensal-Prey with three species Ecosystem", Int. J. of Computational Cognition , vol. 9, pp. 30 – 39, 2011.
N.P. Kumar, "Some Mathematical Models of Ecological Commensalism", Acharya Nagarjuna University, Ph.D. Thesis, 2010.
B.H. Prasad and N.Ch.P.R. Charyulu, "On the Stability of a Four Species: A Prey-Predator-Host-Commensal-Syn Eco-System-VII", Int. J. of Applied Mathematical Analysis and Applications, vol. 6, pp. 85 – 94, 2011.
B.H. Prasad and N.Ch.P.R. Charyulu, "On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-VII", J. of Comm. and Computer, vol. 8, pp. 415 – 421, 2011.
B.H. Prasad and N.Ch.P.R. Charyulu, "On the Stability of a typical three species syn eco-system", Int. J. of Mathematical Archive, vol. 3, pp. 3583 – 3601, 2012.
B.H. Prasad and N.Ch.P.R. Charyulu, "On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-VI", Matematika, vol. 28, pp. 181 – 192, 1012.
B.H. Prasad and N.Ch.P.R. Charyulu, "Global Stability of Four Species Syn Eco-System: A Prey-Predator-Host-Commensal - A Numerical Approach", Int. Journal of Mathematics and Computer Applications Research, vol. 3, pp. 275 – 290, 2013.
B.H. Prasad and N.Ch.P.R. Charyulu, "Discrete Model of Commensalism Between Two Species", International Journal of Modern Education and Computer Science, vol. 8, pp. 40 – 46, 2012.
B.H. Prasad, "A Discrete Model of a Typical Three Species Syn- Eco – System with Unlimited Resources for the First and Third Species", Asian Academic Research Journal of Multidisciplinary, vol. 1, pp. 36 – 46, 2014.
B.H. Prasad, "On the Stability of a Three Species Syn-Eco-System with Mortality Rate for the Second Species", International Journal of Social Science & Interdisciplinary Research, vol. 3, pp. 35 – 45, 2014.
Q. Din and E.M. Elsayed, "Stability Analysis of a Discrete Ecological Model", Computational Ecology and Software, vol. 4, pp. 89 – 103, 1014.
D.R. Kiran, B.R. Reddy and N.Ch.P.R. Charyulu, "Discrete Time Stability Analysis of a Three Species Eco-System", Universal J. of Applied Mathematics, vol. 2, pp.161 – 169, 1014.