Dynamical behavior of systems of two phytoplankton and one zooplankton populations with toxin producing phytoplankton. (26th January 2017)

• Record Type: Journal Article
• Authors: De Silva, Mihiri; Jang, Sophia R.‐J.
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 12(2017)
• Page Start: 4295
• Page End: 4309
• Publication Date: 2017-01-26
• Subjects: phytoplankton -- zooplankton -- mutual interference -- uniform persistence -- periodic forcing; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4305
• Languages: English
• ISSNs: 0170-4214

Abstract

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. Copyright © 2017 John Wiley & Sons, Ltd.