Research Journal of Science and Technology

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Dynamics of Three Species Food Chain Model with Neutralism and Ammensalism


Affiliations
1 Vidya Jyothi Institute of Technology, Hyderabad, India
2 VITS, Hyderabad, India
     

   Subscribe/Renew Journal


The present investigation is an analytical study of three species system comprising two neutral species (First species N1 and Second species N2), which are ammensal on the third species (N3). The model is represented by a system of three first order non-linear ordinary differential equations. Interior equilibrium point is identified and the stability of interior equilibrium point was discussed using Routh-Hurwitz criterion. Further solutions of quasi-linearized equations are identified and the global stability is discussed by Lyapunov's function and the results are simulated by numerical examples using MatLab.

Keywords

Neutralism, Ammensalism, Interior Equilibrium Point, Global Stability, Lyapunov Function.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Lotka A. J. 1925. Elements of Physical Biology, Williams and Wilking, Baltimore.

  • Voltera V, Leconseen La Theori Mathematique De La Leitte Pou Lavie, Gauthier-Villars, Paris, 1931.

  • Meyer. W. J 1925, Concepts of Mathematical Modeling, McGraw-Hill.

  • Cushing. J. N. 1977 Integro-Differential Equations and Delay Models in Population Dynamics. Lecture Notes in Bio-Mathematics. Vol. 20. Springer Verlag.

  • Kapur. J. N. 1985. Mathematical Modeling in Biology Affiliated East West.

  • Kapur. J. N. 1985. Mathematical Modeling, Wiley Easter.

  • Freedman. H. I, Deterministic Mathematical Models in Population Ecology, Decker, New York, 1980.

  • Lakshmi Narayan K, 2005. A Mathematical Steady of a Prey-Predator Ecological Model with a Partial Cover and Alternate food for the Predator, Ph. D. Thesis. J. N. T. University, India.

  • Lakshmi Narayan K and Pattabhiramacharyulu N. Ch, 2007. A Prey-Predator Model with Cover for Prey and Alternate food for the Predator and Time Delay, International Journal of Scientific Computing 1:7-14.

  • Papa Rao. A. V, Lakshmi Narayan. K, Bathul. S. 2012, A Three Species Ecological Model with a Prey, Predator and a Competitor to both the Prey and Predator, International Journal of Mathematics and Scientific Computing ( ISSN: 2231-5330), Vol-2, No. 1, 2012.

  • Kondala Rao K, Lakshmi Narayan K, 2015. Stability Analysis of Ammensal model Comprising Humans, Plants and Birds with Harvesting, Global Journal of Pure and Applied Mathematics (GJPAM), volume 11, Issue 2 (2015 Special issue) pp 115-120, ISSN: 0973-1768.

  • Kondala Rao K and Lakshmi Narayan K, 2016. Dynamics of three species food chain model with harvesting and the paper was published in proceedings of “The 10th International Conference of IMBIC on Mathematical Sciences for Advancement of Science and Technology” (MSAST-2016) with ISBN No: 978-81-925832-4-2.

  • Papa Rao. A. V, Lakshmi Narayan K, 2016. A Prey, Predator and a Competitor to the Predator Model with Gestation Period and the paper was published in proceedings of “The 10th International Conference of IMBIC on Mathematical Sciences for Advancement of Science and Technology” (MSAST-2016) with ISBN No: 978-81-925832-4-2.


Abstract Views: 208

PDF Views: 0




  • Dynamics of Three Species Food Chain Model with Neutralism and Ammensalism

Abstract Views: 208  |  PDF Views: 0

Authors

K. Kondala Rao
Vidya Jyothi Institute of Technology, Hyderabad, India
K. Lakshmi Narayan
VITS, Hyderabad, India

Abstract


The present investigation is an analytical study of three species system comprising two neutral species (First species N1 and Second species N2), which are ammensal on the third species (N3). The model is represented by a system of three first order non-linear ordinary differential equations. Interior equilibrium point is identified and the stability of interior equilibrium point was discussed using Routh-Hurwitz criterion. Further solutions of quasi-linearized equations are identified and the global stability is discussed by Lyapunov's function and the results are simulated by numerical examples using MatLab.

Keywords


Neutralism, Ammensalism, Interior Equilibrium Point, Global Stability, Lyapunov Function.

References