Fractional order oxygen-plankton system under climate change

Area of Science:

• Marine Biology
• Climate Science
• Mathematical Modeling

Background:

• Global climate change alters ocean conditions, affecting marine life.
• Phytoplankton form the base of marine food webs and are vital for oxygen production.
• Ocean warming impacts phytoplankton's photosynthetic rates and oxygen output.

Purpose of the Study:

• To analyze a fractional mathematical model of oxygen-phytoplankton-zooplankton dynamics under climate change.
• To investigate the influence of temperature-dependent photosynthesis on marine ecosystems.
• To compare the fractional model's predictions with classical models.

Main Methods:

• Utilized a Caputo fractional derivative to model oxygen-phytoplankton-zooplankton interactions.
• Incorporated a temperature function to represent the impact of global warming on photosynthesis.
• Applied local Lipschitz conditions to prove the existence and uniqueness of solutions.
• Compared fractional-order results with integer-order derivatives as the fractional order approached one.

Main Results:

• The fractional model demonstrated increased species sustainability compared to classical models.
• Global warming's effect on oxygen production was found to be severe.
• Simulations indicated potential oxygen depletion and plankton extinction.

Conclusions:

• Fractional calculus provides a novel approach to modeling climate change impacts on marine ecosystems.
• Warming oceans pose a significant threat to marine food webs due to oxygen depletion.
• The study highlights the vulnerability of phytoplankton to rising ocean temperatures.