Modelling of phytoplankton allelopathy with Monod-Haldane-type functional response--a mathematical study

Area of Science:

• Ecology
• Mathematical Biology
• Oceanography

Background:

• Phytoplankton blooms are critical ecological events.
• Understanding bloom dynamics requires robust mathematical models.
• Toxicity effects, particularly from phytoplankton, influence zooplankton grazing and bloom termination.

Purpose of the Study:

• To analyze the stability of equilibrium points in a three-tier phytoplankton-zooplankton-nutrient model.
• To investigate the role of a toxification process, mediated by phytoplankton toxicity, in bloom formation and termination.
• To explore Hopf-bifurcation and chaotic dynamics within the model.

Main Methods:

• Development of a three-tier mathematical model (phytoplankton, zooplankton, nutrient).
• Analysis of equilibrium point stability and Hopf-bifurcation.
• Incorporation of a Monod-Haldane grazing function to represent zooplankton response to phytoplankton toxicity.
• Extensive numerical simulations to validate analytical findings.

Main Results:

• Stability analysis of various equilibrium points was performed.
• Hopf-bifurcation around the coexisting equilibrium point was investigated.
• The model demonstrated chaotic oscillations for specific parameter values, influenced by the toxicity-dependent grazing function.
• Numerical simulations confirmed the potential for complex dynamics.

Conclusions:

• The three-tier model effectively captures bloom dynamics influenced by phytoplankton toxicity.
• Zooplankton grazing, modeled by the Monod-Haldane function, plays a crucial role in bloom termination.
• The system can exhibit chaotic behavior, highlighting the complexity of aquatic ecosystems.