Dynamical behavior of systems of two phytoplankton and one zooplankton populations with toxin producing phytoplankton

Mihiri De Silva; Sophia R.J. Jang

doi:10.1002/mma.4305

Dynamical behavior of systems of two phytoplankton and one zooplankton populations with toxin producing phytoplankton

Mihiri De Silva, Sophia R.J. Jang

Mathematics and Statistics

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10 Scopus citations

Abstract

Three-compartment mathematical models of non-toxic phytoplankton (NTP), toxin producing phytoplankton (TPP), and zooplankton are proposed to explore the role of TPP in algal blooms. The mutual interference between predator zooplankton and avoidance of TPP by zooplankton are incorporated into the model. The NTP and TPP engage in exploit competition and the toxin produced by TPP has no effect on NTP. Using the concept of uniform persistence, we establish coexistence of NTP, TPP, and zooplankton in certain parameter regimes. We study the effects of mutual interference and avoidance by zooplankton upon the population interactions. In addition to the toxin producing mechanism, it is concluded that mutual interference of zooplankton is an important factor for diminishing harmful blooms.

Original language	English
Pages (from-to)	4295-4309
Number of pages	15
Journal	Mathematical Methods in the Applied Sciences
Volume	40
Issue number	12
DOIs	https://doi.org/10.1002/mma.4305
State	Published - Aug 2017

Keywords

mutual interference
periodic forcing
phytoplankton
uniform persistence
zooplankton

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10.1002/mma.4305

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abstract = "Three-compartment mathematical models of non-toxic phytoplankton (NTP), toxin producing phytoplankton (TPP), and zooplankton are proposed to explore the role of TPP in algal blooms. The mutual interference between predator zooplankton and avoidance of TPP by zooplankton are incorporated into the model. The NTP and TPP engage in exploit competition and the toxin produced by TPP has no effect on NTP. Using the concept of uniform persistence, we establish coexistence of NTP, TPP, and zooplankton in certain parameter regimes. We study the effects of mutual interference and avoidance by zooplankton upon the population interactions. In addition to the toxin producing mechanism, it is concluded that mutual interference of zooplankton is an important factor for diminishing harmful blooms.",

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AB - Three-compartment mathematical models of non-toxic phytoplankton (NTP), toxin producing phytoplankton (TPP), and zooplankton are proposed to explore the role of TPP in algal blooms. The mutual interference between predator zooplankton and avoidance of TPP by zooplankton are incorporated into the model. The NTP and TPP engage in exploit competition and the toxin produced by TPP has no effect on NTP. Using the concept of uniform persistence, we establish coexistence of NTP, TPP, and zooplankton in certain parameter regimes. We study the effects of mutual interference and avoidance by zooplankton upon the population interactions. In addition to the toxin producing mechanism, it is concluded that mutual interference of zooplankton is an important factor for diminishing harmful blooms.

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Dynamical behavior of systems of two phytoplankton and one zooplankton populations with toxin producing phytoplankton

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Keywords

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