Mathematical analysis of a nutrient–plankton system with delay

A mathematical model describing the interaction of nutrient–plankton is investigated in this paper. In order to account for the time needed by the phytoplankton to mature after which they can release toxins, a discrete time delay is incorporated into the system. Moreover, it is also taken into account discrete time delays which indicates the partially recycled nutrient decomposed by bacteria after the death of biomass. In the first part of our analysis the sufficient conditions ensuring local and global asymptotic stability of the model are obtained. Next, the existence of the Hopf bifurcation as time delay crosses a threshold value is established and, meanwhile, the phenomenon of stability switches is found under certain conditions. Numerical simulations are presented to illustrate the analytical results.

• Publication year

  2016

• Venue

  SpringerPlus

• Publication date

  2016-07-11

• Fields of study

  Mathematics, Medicine, Environmental Science

• Identifiers
  DOI 10.1186/s40064-016-2435-7PMID 27462503PMCID 4940349
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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