American Journal of Applied Mathematics

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

Received: 22 August 2014    Accepted: 09 September 2014    Published: 20 September 2014
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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.

DOI 10.11648/j.ajam.20140205.11
Published in American Journal of Applied Mathematics (Volume 2, Issue 5, October 2014)
Page(s) 149-154
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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), 2024. Published by Science Publishing Group

Keywords

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

References
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[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).
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[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).
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Author Information
  • Department of Mathematics, The Madura College, Madurai, Tamil Nadu, India

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

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  • 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

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    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

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    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

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  • @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://download.sciencepg.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}
    }
    

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    AU  - Vembu Ananthaswamy
    AU  - Lucas Sahaya Amalraj
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    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.
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