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Stability analysis of a continuous model of mutualism with delay dynamics
Roberts, Jason A. Joharjee, Najwa G.
Roberts, Jason A.
Joharjee, Najwa G.
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2016-05-31
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Abstract
In this paper we introduce delay dynamics to a coupled system of
ordinary differential equations which represent two interacting species
exhibiting facultative mutualistic behaviour. The delays are represen-
tative of the beneficial effects of the indirect, interspecies interactions
not being realised immediately. We show that the system with delay
possesses a continuous solution, which is unique. Furthermore we show
that, for suitably-behaved, positive initial functions that this unique
solution is bounded and remains positive, i.e. both of the components
representing the two species remain greater than zero. We show that
the system has a positive equilibrium point and prove that this point
is asymptotically stable for positive solutions and that this stability
property is not conditional upon the delays.
Citation
Roberts, J. A., & Joharjee, N. G. (2016). Stability analysis of a continuous model of mutualism with delay dynamics. International Mathematical Forum, 11(10), 463-473. http://dx.doi.org/10.12988/imf.2016.616
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Hikari
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International Mathematical Forum
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Article
Language
en
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1312-7594