Role of delay on planktonic ecosystem in the presence of a toxic producing phytoplankton
type: Item
instance of: scholarly article
title: Role of delay on planktonic ecosystem in the presence of a toxic producing phytoplankton
zbMATH Open document ID: 1239.34099
DOI: 10.1155/2011/603183
author: Swati Khare
author: O. P. Misra
author: Chhatrapal Singh
author: J. Dhar
published in: International Journal of Differential Equations
publication date: 2012-03-08T00:00:00Z
review text: Summary: A mathematical model is proposed to study the role of distributed delay on planktonic ecosystem in the presence of a toxic producing phytoplankton. The model includes three state variables, namely, nutrient concentration, phytoplankton biomass, and zooplankton biomass. The release of toxic substance by phytoplankton species reduces the growth of zooplankton and this plays an important role in plankton dynamics. In this paper, we introduce a delay (time-lag) in the digestion of nutrient by phytoplankton. The stability analysis of all the feasible equilibria are studied and the existence of Hopf bifurcation for the interior equilibrium of the system is explored. From the above analysis, we observe that the supply rate of nutrient and delay parameter play important role in changing the dynamical behaviour of the underlying system. Further, we derive the explicit algorithm which determines the direction and the stability of Hopf bifurcation solution. Finally, numerical simulation is carried out to support the theoretical result.
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K21
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6013206
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/603183
OpenAlex ID: W2155439371
Wikidata QID: Q58686808
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description: scientific article; zbMATH DE number 6013206