Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method

Vembu Ananthaswamy; Lucas Sahaya Amalraj

doi:doi:10.11648/j.ajam.20140205.11

| Peer-Reviewed

Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method

Vembu Ananthaswamy, Lucas Sahaya Amalraj

Published in American Journal of Applied Mathematics (Volume 2, Issue 5)

Received: 22 August 2014 Accepted: 9 September 2014 Published: 20 September 2014

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper a mathematical commensal-host ecological model with replenishment rate for both species is discussed. This model is characterized by a pair of first order non-linear coupled differential equations. The non-linear coupled system-equations are solved analytically by using Homotopy perturbation method. Further, our results are compared with the previous work and a satisfactory agreement is noted.

Published in	American Journal of Applied Mathematics (Volume 2, Issue 5)
DOI	10.11648/j.ajam.20140205.11
Page(s)	149-154
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Mathematical Model, Commensal, Host, Replenishment Rate, Non-Linear Differential Equations, Homotopy Perturbation Method

References

[1]	N. Phani Kumar, C. Srinivasa kumar and N.Ch. Pattabhi Ramacharyulu, “A recursive procedure for commensal-host ecological model with replenishment rate for both the species- A numerical approach, ARPN Journal of Engineering and Applied Sciences, Vol. 5, No.10 (2010).
[2]	B. Bhaskara Rama Sarma. N.Ch Pattabhi Ramacharyulu and S.V.N. Lalitha, “A recursive procedure for two species competing eco system with decay and replenishment for one specie”, Acta ciencia Indica. Xxxv M. (2): 487-496 (2009).
[3]	J.M. Cushing, “Integro - differential equations and delay models in population dynamics”, Lect. Notes in Biomathematics. Vol. 20, springer - reflag, Heidelbegh 9.(1977).
[4]	J.N. Kapur, “Mathematical models in biology and medicine”, Affiliated East-West 9, (1985).
[5]	W.E. Langlois and R.S. Rivlin, “Steady flow of slightly visco-elastic fluids”, (Doctoral thesis of W-Elanglois), Brown universality, (1957).
[6]	W.J. Meyer, “Concepts of mathematical modeling”, Mc-Grawhill, (1985).
[7]	N. Phanikumar and N. Ch. Pattabhi Ramacharyulu, “On the stability of a commesal-host harvested species pair with limited resources”, Communicated to International journal of computational cognition.
[8]	N.C. Srinvias, “Some mathematical aspects of modeling in bio-medical sciences”, Ph.D. thesis, submitted to Kakatiya university, (1991).
[9]	Q.K. Ghori, M. Ahmed, and A. M. Siddiqui, “Application of Homotopy perturbation method to squeezing flow of a newtonian fluid”, Int. J. Non-linear Sci. Numer. Simulat, 8 179-184 (2007).
[10]	T. Ozis, and A. Yildirim, “A comparative study of He’s Homotopy perturbation method for determining frequency-amplitude relation of a non-linear oscillator with discontinuities”, Int. J. Nonlinear Sci. Numer. Simulat, 8, 243-248 (2007).
[11]	S. J. Li, and Y. X. Liu, “An improved approach to non-linear dynamical system identification using PID neural networks”, Int. J. Non-linear Sci. Numer. Simulat, 7, 177-182 (2006).
[12]	M. M. Mousa, S. F. Ragab, and Z. Nturforsch , “Application of the Homotopy perturbation method to linear and non-linear schrödinger equations“,. Zeitschrift für naturforschung“, 63, 140-144 (2008).
[13]	J.H. He, “Homotopy perturbation technique”, Comp Meth. Appl. Mech. Eng, 178, 257-262 (1999).
[14]	J. H. He, “Homotopy perturbation method: a new non-linear analytical technique”, Appl. Math. Comput, 135, 73-79(2003).
[15]	J. H. He, “A simple perturbation approach to blasius equation”, Appl. Math. Comput, 140, 217-222 (2003).
[16]	P.D. Ariel ,“Alternative approaches to construction of Homotopy perturbation algorithms”, Nonlinear. Sci. Letts. A., 1, 43-52 (2010).
[17]	V. Ananthaswamy, and L. Rajendran, “Analytical solution of non-linear kinetic equation in a porous pellet”, Global journal of pure and applied mathematics, Vol.8, no. 2, 101-111 (2012).
[18]	V. Ananthaswamy and L. Rajendran, “Analytical solution of two-point non-linear boundary value problems in a porous catalyst particles”, International Journal of Mathematical Archive, 3 (3), 810-821 (2012).
[19]	V.Ananthaswamy and L. Rajendran, “Analytical solution of non-isothermal diffusion-reaction processes and effectiveness factors”, ISRN Physical Chemistry, Hindawi publishing corporation, 2013, Article ID 487240, 1-14 (2013).

Cite This Article

Plain Text BibTeX RIS

APA Style

Vembu Ananthaswamy, Lucas Sahaya Amalraj. (2014). Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method. American Journal of Applied Mathematics, 2(5), 149-154. https://doi.org/10.11648/j.ajam.20140205.11

Copy | Download

ACS Style

Vembu Ananthaswamy; Lucas Sahaya Amalraj. Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method. Am. J. Appl. Math. 2014, 2(5), 149-154. doi: 10.11648/j.ajam.20140205.11

Copy | Download

AMA Style

Vembu Ananthaswamy, Lucas Sahaya Amalraj. Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method. Am J Appl Math. 2014;2(5):149-154. doi: 10.11648/j.ajam.20140205.11

Copy | Download

@article{10.11648/j.ajam.20140205.11,
  author = {Vembu Ananthaswamy and Lucas Sahaya Amalraj},
  title = {Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {5},
  pages = {149-154},
  doi = {10.11648/j.ajam.20140205.11},
  url = {https://doi.org/10.11648/j.ajam.20140205.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140205.11},
  abstract = {In this paper a mathematical commensal-host ecological model with replenishment rate for both species is discussed. This model is characterized by a pair of first order non-linear coupled differential equations. The non-linear coupled system-equations are solved analytically by using Homotopy perturbation method. Further, our results are compared with the previous work and a satisfactory agreement is noted.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method
AU  - Vembu Ananthaswamy
AU  - Lucas Sahaya Amalraj
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140205.11
DO  - 10.11648/j.ajam.20140205.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 149
EP  - 154
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140205.11
AB  - In this paper a mathematical commensal-host ecological model with replenishment rate for both species is discussed. This model is characterized by a pair of first order non-linear coupled differential equations. The non-linear coupled system-equations are solved analytically by using Homotopy perturbation method. Further, our results are compared with the previous work and a satisfactory agreement is noted.
VL  - 2
IS  - 5
ER  -

Copy | Download

Author Information

Vembu Ananthaswamy

Department of Mathematics, The Madura College, Madurai, Tamil Nadu, India
Lucas Sahaya Amalraj

Department of Mathematics, Raja Doraisingam Government Arts College, Sivagangai District, Tamil Nadu, India

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Vembu Ananthaswamy, Lucas Sahaya Amalraj. (2014). Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method. American Journal of Applied Mathematics, 2(5), 149-154. https://doi.org/10.11648/j.ajam.20140205.11

Copy | Download

ACS Style

Vembu Ananthaswamy; Lucas Sahaya Amalraj. Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method. Am. J. Appl. Math. 2014, 2(5), 149-154. doi: 10.11648/j.ajam.20140205.11

Copy | Download

AMA Style

Vembu Ananthaswamy, Lucas Sahaya Amalraj. Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method. Am J Appl Math. 2014;2(5):149-154. doi: 10.11648/j.ajam.20140205.11

Copy | Download

@article{10.11648/j.ajam.20140205.11,
  author = {Vembu Ananthaswamy and Lucas Sahaya Amalraj},
  title = {Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method},
  journal = {American Journal of Applied Mathematics},
  volume = {2},
  number = {5},
  pages = {149-154},
  doi = {10.11648/j.ajam.20140205.11},
  url = {https://doi.org/10.11648/j.ajam.20140205.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140205.11},
  abstract = {In this paper a mathematical commensal-host ecological model with replenishment rate for both species is discussed. This model is characterized by a pair of first order non-linear coupled differential equations. The non-linear coupled system-equations are solved analytically by using Homotopy perturbation method. Further, our results are compared with the previous work and a satisfactory agreement is noted.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Analytical Expressions for Commensal-Host Ecological Model: Homotopy Perturbation Method
AU  - Vembu Ananthaswamy
AU  - Lucas Sahaya Amalraj
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140205.11
DO  - 10.11648/j.ajam.20140205.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 149
EP  - 154
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140205.11
AB  - In this paper a mathematical commensal-host ecological model with replenishment rate for both species is discussed. This model is characterized by a pair of first order non-linear coupled differential equations. The non-linear coupled system-equations are solved analytically by using Homotopy perturbation method. Further, our results are compared with the previous work and a satisfactory agreement is noted.
VL  - 2
IS  - 5
ER  -

Copy | Download