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

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Authors

  • B. Hari Prasad
     ,IN

DOI:

https://doi.org/10.18311/jims/2019/22576

Keywords:

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

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 roots 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.

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Published

2018-12-12

How to Cite

Hari Prasad, B. (2018). Stability Analysis of a Three Species Non-linear Eco-system with Restricted Resources. The Journal of the Indian Mathematical Society, 86(1-2), 126–136. https://doi.org/10.18311/jims/2019/22576

Issue

Volume 86, Issue 1-2, January-June 2019

Section

Articles

License

Copyright (c) 2018 B. Hari Prasad

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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