Modeling the dynamics of a marine system using the fractional order approach to assess its susceptibility to global warming
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Keywords:
Caputo fractional derivatives, simulation, oxygen, plankton, fish, global warming, numerical resultsAbstract
In the marine ecosystem, phytoplankton plays a vital role as the primary supplier of oxygen, contributing to 50\% of the total oxygen production. Not only does it serve as a significant source of food for other species, but it also sustains life in the ocean. However, the rising ocean temperatures caused by global warming have severely hindered the ability of phytoplankton to generate oxygen. Furthermore, fishes are crucial consumers of oxygen within the marine ecosystem. This research paper presents a model that intricately connects the dynamics of oxygen, phytoplankton, zooplankton, and fish using the Caputo fractional derivative. The model aims to examine the impact of global warming on the collective dynamics by considering the relationship between the rate of oxygen generation, temperature, and time. The paper establishes the existence and uniqueness of solutions and also analyzes the stability of equilibrium points. Numerical simulations are conducted to demonstrate the impact of fractional derivatives and global warming on oxygen depletion and species extinction.
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