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Discrete modeling of the three species syn-ecosystem with unlimited resources

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Języki publikacji
EN
Abstrakty
EN
In this paper, the three species syn-ecosystem is comprised of a commensal (S1), two hosts S2 and S3, i.e. S2 and S3 both benefit S1 without getting themselves affected 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 unlimited resources. The basic equations for this model constitute as three first order non-linear coupled ordinary difference equations. All possible equilibrium states are identified based on the model equations at two stages and criteria for their stability are discussed. Further, the numerical solutions are computed for specific values of the various parameters and the initial conditions.
Słowa kluczowe
Rocznik
Strony
85--93
Opis fizyczny
Bibliogr. 21 poz., rys.
Twórcy
autor
  • Department of Mathematics, Chaitanya Degree and PG College (Autonomous) Hanamkonda, Telangana State, India-506 001
Bibliografia
  • [1] Lotka A.J., Elements of Physical Biology, Williams and Wilking, Baltimore 1925.
  • [2] Svirezhev Yu.M., Logofet D.O., Stability of Biological Community, MIR, Moscow 1983.
  • [3] Volterra V., Leconssen La Theorie Mathematique De La Leitte Pou Lavie, Gauthier-Villars, Paris 1931.
  • [4] Rogers D.J., Hassell M.P., General models for insect parasite and predator searching behavior, Interference, Journal Anim. Ecol. 1974, 43, 239-253.
  • [5] Varma V.S., A note on exact solutions for a special prey - predator or competing species system, Bull. Math. Biol. 1977, 39, 619-622.
  • [6] Veilleux B.G., An analysis of the predatory interaction between Paramecium & Didinium, Journal Anim. Ecol. 1979, 48, 787-803.
  • [7] Colinvaux A.P., Ecology, John Wiley, New York 1986.
  • [8] Smith J.M., Models in Ecology, Cambridge University Press, Cambridge 1974.
  • [9] Kapur J.N., Mathematical Modeling in Biology & Medicine, Affiliated East West, 1985.
  • [10] Kushing J.M., Integro-Differential Equations and Delay Models in Population Dynamics, Lecture Notes in Bio-Mathematics, Springer Verlag, 1977, 20.
  • [11] Meyer W.J., Concepts of Mathematical Modeling, McGraw-Hill, 1985.
  • [12] Pielou E.C., Mathematical Ecology, John Wiley and Sons, New York 1977.
  • [13] Srinivas N.C., Some Mathematical Aspects of Modeling in Bio-medical Sciences, Ph.D Thesis, Kakatiya University, 1991.
  • [14] Narayan K.L., Pattabhiramacharyulu N.Ch., A prey-predator model with cover for prey and alternate food for the predator and time delay, Int. Journal of Scientific Computing 2007, 1, 7-14.
  • [15] Acharyulu K.V.L.N., Pattabhiramacharyulu N.Ch., An enemy - ammensal species pair with limited resources - a numerical study, Int. Journal Open Problems Compt. Math. 2010, 3, 339-356.
  • [16] Acharyulu K.V.L.N., Pattabhiramacharyulu N.Ch., An ammensal-prey with three species ecosystem, International Journal of Computational Cognition 2011, 9, 30-39.
  • [17] Kumar N.P., Some Mathematical Models of Ecological Commensalism, Ph.D. Thesis, Acharya Nagarjuna University, 2010.
  • [18] Prasad B.H., On the stability of a three species syn-eco-system with mortality rate for the second species, Int. Journal of Social Science & Interdisciplinary Research 2014, 3, 35-45.
  • [19] Prasad B.H., The stability analysis of a three species syn-eco-system with mortality rates, Contemporary Mathematics and Statistics 2014, 2, 76-89.
  • [20] Prasad B.H., A study on discrete model of three species syn-eco-system with limited resources, Int. Journal Modern Education and Computer Science 2014, 11, 38-44.
  • [21] Prasad B.H., 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 2014, 1, 36-46.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fc66f3f9-c06b-45cc-8fc5-caf57803f057
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