Global stability of two-species mutualism model with proportional harvesting

Ahmad, Rusliza

International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 7 (July 2017), Pages: 74-79

Title: Global stability of two-species mutualism model with proportional harvesting

Author(s): Rusliza Ahmad *

Affiliation(s):

Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Perak Branch, Tapah Campus, 35400 Tapah, Perak, Malaysia

https://doi.org/10.21833/ijaas.2017.07.011

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Abstract:

This paper deals with the study on a mathematical model consisting of mutualistic interactions among two-species with proportional harvesting. Harvesting function is introduced to describe the rate of removal of the species. The local stability analysis shows that the unique positive equilibrium point is asymptotically stable when certain conditions are satisfied. Global stability is discussed by constructing Lyapunov function. It has been shown that the unique positive equilibrium point is globally asymptotically stable. Finally, numerical simulations supporting theoretical results are also included.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Global stability, Lyapunov function, Mutualism model, Proportional harvesting

Article History: Received 2 March 2017, Received in revised form 28 May 2017, Accepted 7 June 2017

Digital Object Identifier:

https://doi.org/10.21833/ijaas.2017.07.011

Citation:

Ahmad R (2017). Global stability of two-species mutualism model with proportional harvesting. International Journal of Advanced and Applied Sciences, 4(7): 74-79

http://www.science-gate.com/IJAAS/V4I7/Ahmad.html

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