Discrete Model of a Prey-Predator Eco-System with Mortality Rates and Limited-Unlimited Resources

B. Hari Prasad

Abstract


The present paper is devoted to an investigation on a discrete model of two interacting species a prey-predator eco-system with limited - unlimited resources and mortality rates. The system comprises of a prey (S1), a predator (S2) that survives upon S1. The basic equations for this model constitute as two first order non-linear coupled ordinary difference equations. All possible equilibrium points are identified based on the model equations and criteria for their stability are discussed. The model would be stable if absolute value of each of the eigen values of the characteristic equation is less than one.

Full Text:

PDF

References


Yu. M. Svirezhev and D. O. Logofet, Stability of Biological Community, MIR, Moscow, 1983.

V. Volterra, Leconssen La Theorie Mathematique De La Leitte Pou Lavie, Gauthier-Villars, Paris, 1931.

D. J. Rogers and M. P. Hassell, General models for insect parasite and predator searching behavior: Interference, Journal Anim. Ecol., 1974, 43, 239 - 253.

V. S. Varma, A note on Exact solutions for a special Prey - Predator or competing species system, Bull. Math. Biol., 1977, 39, 619 - 622.

B. G. Veilleux, An analysis of the predatory interaction between paramecium & Didinium, Journal Anim. Ecol., 1979, 48, 787 - 803.

A. P. Colinvaux, Ecology, John Wiley, New York, 1986.

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

J. N. Kapur, Mathematical Modeling in Biology & Medicine, Affiliated East West,1985.

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

W. J. Meyer, Concepts of Mathematical Modeling, Mc.Grawhill, 1985.

E. C. Pielou, Mathematical Ecology, John Wiley and Sons, New York, 1977.

N. C. Srinivas, Some Mathematical Aspects of Modeling in Bio-medical Sciences, Kakatiya University, Ph.D Thesis, 1991.

K. L. Narayan and N. Ch. Pattabhiramacharyulu, 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.

K. V. L. N. Acharyulu and N. Ch. Pattabhiramacharyulu, An Enemy- Ammensal Species Pair With Limited Resources - A Numerical Study, Int. Journal Open Problems Compt. Math., 2010,3, 339-356.

B. H. Prasad, Mathematical Modeling on Ecosystem Consisting of Two Hosts and One Commensal with Mortality Rates for the First and Third Species, World Journal of Modelling and Simulation, 2017, 13(3), 163-172.

B. H. Prasad, A Study on a Four Species Syn-Eco-System Consisting of Host-Commensal, Prey-Predator and Co-Operation with Mortality Rates, Int. Journal of Advanced Research in Computer Science and Software Engineering, 2017, 07(6), 474-479.

B. H. Prasad, A Study on Host Mortality Rate of a Three Species Multi Ecology with Unlimited Resources for the First Species. Journal of Asian Scientific Research, 2017, 07(4), 134-144.

B. H. Prasad, Stability Analysis of a Three Species Syn-Eco-System with Mortality Rates for the First and Third Species. Int. Journal of Physics and Mathematical Sciences, 2016, 06(4), 27-35.

B. H. Prasad, K. S. Rani and P. S. R. Chandra Rao, A Study on Discrete Model of Three Species Syn-Eco-System with Unlimited Resources for the First species. International Journal of Mathematical Sciences. Technology and Humanities, 2016, 6(1), 01-21.

B. H. Prasad, A Study on Discrete Model of a Prey-Predator Eco-System with Limited and Unlimited Resources. The Journal of Indian Mathematical Society, 2015, 82(3-4), 169-179.

B. H. Prasad, A Study on the Discrete Model of Three Species Syn-Eco-System with Unlimited Resources. Journal of Applied Mathematics and Computational Mechanics, 2015, 14(2), 85-93.

B. H. Prasad, 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.

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, 2014, 1, 36-46.

B. H. Prasad, A Discrete Model of Three Species Syn-Eco-System with Unlimited Resources for the Second and Third Species. ZENITH International Journal of Multidisciplinary Research, 2013, 3(12), 42-51.

B. H. Prasad and N. Ch. Pattabhiramacharyulu, On the Stability of a Four Species Syn Eco-System with Commensal Prey Predator Pair with Prey Predator Pair of Hosts-VI. Matematika, 2012, 28(2), 181-192.




DOI: https://doi.org/10.23956/ijarcsse.v8i8.830

Refbacks

  • There are currently no refbacks.




© International Journals of Advanced Research in Computer Science and Software Engineering (IJARCSSE)| All Rights Reserved | Powered by Advance Academic Publisher.