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On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay

Author

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  • Mehbuba Rehim
  • Weixin Wu
  • Ahmadjan Muhammadhaji

Abstract

A toxin producing phytoplankton-zooplankton model with inhibitory exponential substrate and time delay has been formulated and analyzed. Since the liberation of toxic substances by phytoplankton species is not an instantaneous process but is mediated by some time lag required for maturity of the species and the zooplankton mortality due to the toxic phytoplankton bloom occurs after some time laps of the bloom of toxic phytoplankton, we induced a discrete time delay to both of the consume response function and distribution of toxic substance term. Furthermore, based on the fact that the predation rate decreases at large toxic-phytoplankton density, the system is modelled via a Tissiet type functional response. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.

Suggested Citation

  • Mehbuba Rehim & Weixin Wu & Ahmadjan Muhammadhaji, 2015. "On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-13, February.
    • Handle: RePEc:hin:jnddns:756315
    DOI: 10.1155/2015/756315
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    Cited by:

    1. Chakraborty, Subhendu & Moorthi, Stefanie D. & Karnatak, Rajat & Feudel, Ulrike, 2022. "Irregular harmful algal blooms triggered by feedback between toxin production and zooplankton feeding," Ecological Modelling, Elsevier, vol. 473(C).
    2. Galina Neverova & Oksana Zhdanova, 2023. "Mathematical Modeling of the Evolutionary Dynamics of a Planktonic Community Using a Discrete-Time Model," Mathematics, MDPI, vol. 11(22), pages 1-24, November.

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