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Review of Information Engineering and Applications

December 2014, Volume 1, 2, pp 55-65

A Study on Commensal Mortality Rate of a Typical Three Species Syn-Eco-System with Unlimited Resources for Commensal

B. Hari Prasad

B. Hari Prasad 1

  1. Department of Mathematics, Chaitanya Degree and PG College (Autonomous), Hanamkonda, Andhra Pradesh, India 1

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Pages: 55-65

DOI: 10.18488/journal.79/2014.1.2/

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The present investigation is on an analytical and numerical study of a typical three species syn-eco system with mortality rate for commensal. The system comprises of a commensal (S1), two hosts S2 and S3 where S2 and S3 both benefit S1, without getting themselves affected either positively or adversely. Further the first species has unlimited resources. The model equations constitute a set of three first order non-linear coupled differential equations. Criteria for the asymptotic stability of all the four equilibrium states are established. Trajectories of the perturbations over the equilibrium states are illustrated. Further the global stability of the system is established with the aid of suitably constructed Liapunov’s function and the numerical solutions for the growth rate equations are computed using Runge-Kutta fourth order scheme.
Contribution/ Originality



  1. A. J. Lotka, Elements of physical biology. Baltimore: Williams and Wilking, 1925.
  2. V. Volterra, A text book of leconssen la theorie mathematique de la leitte pou lavie. Paris: Gauthier-Villars, 1931.
  3. W. J. Meyer, "A text book of concepts of mathematical modeling," Mc.Grawhill, Edn, vol. 3, pp. 139–222, 1985.
  4. J. M. Kushing, "Integro-differential equations and delay models in population dynamics," Lecture Notes in Bio-Mathematics, Springer Verlag, vol. 20, p. 591, 1977.
  5. J. N. Kapur, A text book of mathematical modelling in biology and medicine: Affiliated East West, 1985.
  6. N. C. Srinivas, "Some mathematical aspects of modeling in bio-medical sciences," Ph.D Thesis, Kakatiya University, 1991.
  7. K. L. Narayan and N. C. R. Pattabhi, "A prey-predator model with cover for prey and alternate food for the predator and time delay," International Journal of Scientific Computing, vol. 1, pp. 7–14, 2007.
  8. R. R. Archana, N. C. R. Pattabhi, and B. K. Gandhi, "A stability analysis of two competetive interacting species with harvesting of both the species at a constant rate," Int. Journal of Scientific Computing, vol. 1, pp. 57–68, 2007.
  9. B. R. S. Bhaskara and N. C. R. Pattabhi, "Stability analysis of two species competitive eco-system," Int.J.of Logic Based Intelligent Systems, vol. 2, pp. 79 – 86, 2008.
  10. R. R. Ravindra, "A study on mathematical models of ecological mutualism between two interacting species," Ph.D., Thesis, Osmania University, 2008.
  11. N. K. Phani, "Some mathematical models of ecological commensalism," Ph.D., Thesis, Acharya Nagarjuna University, 2010.
  12. B. P. Hari and N. C. R. Pattabhi, "On the stability of a typical three species syn eco-system," Int. J. of Mathematical Archive, vol. 3, pp. 3583–3601, 2012.
  13. B. P. Hari and N. C. R. Pattabhi, "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, pp. 85–94, 2011.
  14. B. P. Hari and N. C. R. Pattabhi, "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, pp. 65–73, 2010.
  15. B. P. Hari and N. C. R. Pattabhi, "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, pp. 415–421, 2011.
  16. B. P. Hari and N. C. R. Pattabhi, "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, pp. 235–242, 2012.


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