The Journal of the Indian Mathematical Society

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Stability Analysis of a Three Species Non-linear Eco-system with Restricted Resources


Affiliations
1 Department of Mathematics, Chaitanya Group of Colleges (Autonomous), Hanamkonda, India
     

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The aim of this paper is to introduce the model and the study of a three species non linear ecosystem with restricted resources. In this paper, the system comprises of two species hosts S1, S2 and one commensal species S3. Further, S1 and S2 are neutral and all the three species posses restricted resources. Commensalism is a symbiotic interaction between two or more populations which live together, and in which only one of the populations (commensalism) is beneted while the other (host) is not effected. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic ischolar_mains are negative, in case they are real, and have negative real parts, in case they are complex. 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.

Keywords

Commensal, Equilibrium State, Host, Neutral, Stable, Trajectories, Unstable.
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  • N. Arumugam, Concepts of Ecology, Saras Publication, India, (2006).

  • M. Gillman, An Introduction to Mathematical Models in Ecology and Evolution, Wiley-Blackwell, U.K., (2009).

  • M. Kot, Elements of Mathematical Ecology, Cambridge University Press, U.K., (2001).

  • Z. Ma, The Study of Biology Model, Anhui Education Press, China, (1996).

  • J. D. Murray, Mathematical Biology, Springer, New York, (1993).

  • 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, 7(2017), 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, 7(2017), 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, 6(2016), 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, 6(2016), 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, 82(2015), 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, 14(2015), 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, 11(2014), 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, 1(2014), 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, 3(2013), 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, 28(2012), 181-192.

  • P. D. Sharma, Ecology and Environment, Rastogi Publications, India, (2009).

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

  • Sze-Bi Hsu, Mathematical Modeling in Biological Science, Tsing-Hua University, Taiwan, (2004).


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  • Stability Analysis of a Three Species Non-linear Eco-system with Restricted Resources

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Authors

B. Hari Prasad
Department of Mathematics, Chaitanya Group of Colleges (Autonomous), Hanamkonda, India

Abstract


The aim of this paper is to introduce the model and the study of a three species non linear ecosystem with restricted resources. In this paper, the system comprises of two species hosts S1, S2 and one commensal species S3. Further, S1 and S2 are neutral and all the three species posses restricted resources. Commensalism is a symbiotic interaction between two or more populations which live together, and in which only one of the populations (commensalism) is beneted while the other (host) is not effected. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic ischolar_mains are negative, in case they are real, and have negative real parts, in case they are complex. 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.

Keywords


Commensal, Equilibrium State, Host, Neutral, Stable, Trajectories, Unstable.

References