Deterministic and stochastic nutrient-phytoplankton-zooplankton models with periodic toxin producing phytoplankton

Ruey-Jen Jang, Edward Allen

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Deterministic and stochastic models of nutrient-phytoplankton-zooplankton interaction are proposed to investigate the impact of toxin producing phytoplankton upon persistence of the populations. The toxin liberation by phytoplankton is modeled periodically in the deterministic system. We derive two thresholds in terms of the parameters for which both plankton populations can persist if these thresholds are positive. We construct stochastic models with Itô differential equations to model variability in the environment. It is concluded that the input nutrient concentration along with the toxin liberation rate play critical roles in the dynamics of the planktonic interaction. In particular, toxin producing phytoplankton can terminate harmful algal blooms and the planktonic interaction is more stable if either the input nutrient concentration is smaller or if the toxin production rate is larger.

Original languageEnglish
Pages (from-to)52-67
Number of pages16
JournalApplied Mathematics and Computation
StatePublished - Nov 15 2015


  • Itô stochastic differential equations
  • Phytoplankton
  • Uniform persistence
  • Zooplankton


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