Global stability of a delay differential equations model of plankton allelopathy

Global stability of a delay differential equations model of plankton allelopathy

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Article ID: iaor20122099
Volume: 218
Issue: 13
Start Page Number: 7155
End Page Number: 7163
Publication Date: Mar 2012
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: biology
Abstract:

In this paper, we consider a delay differential equations model of plankton allelopathy. Using an iterative method, the global stability of the interior equilibrium point of the system is investigated, which shows that toxic substances are harmless for the stability of the interior equilibrium point. The results we obtained improve and complement those of Chattopadhyay [J. Chattopadhyay, Effect of toxic substances on a two‐species competitive system, Ecol. Model. 84 (1996) 287–289], Samanta [G.P. Samanta, A two‐species competitive system under the influence of toxic substances, Appl. Math. Comput. 216 (2010) 291–299] and Mukhopadhyay et al. [A. Mukhopadhyay, J. Chattopadhyay, P.K. Tapaswi, A delay differential equations model of plankton allelopathy, Math. Biosci. 149 (1998) 167–189]. We also present some examples to verify our main result.

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