Environmental Change Effect on Oxygen-Plankton System: Mathematical Approach

Abstract

Oxygen loss in a water body is a significant environmental issue, also accountable for the extinction of marine fauna. Therefore, oxygen production by marine phytoplankton photosynthesis is thought to hold the key to the underlying structure of oxygen dynamics in the marine ecosystem. However, the oxygen concentration is not only determined by primary production. This oxygen concentration also depends on its consumption such as biochemical reaction in the water body, consumption by marine animals, water-air reaeration, etc. Plankton respiration is one of the these factors that play an important role in water body oxygen concentration. Therefore, in this work, this issue is addressed theoretically by considering the oxygen-phytoplankton-zooplankton model to make an insight into system dynamics under the effect of changing environmental condition on phytoplankton growth rate. The difference between this work and the literature is the specific paremeter value of $B$, suggesting that the changing environment has an effect on the growth rate of phytoplankton. A nonlinear mathematical model is considered to investigate the effect of temperature on oxygen-plankton dynamics with Holling Type II function as respiration of plankton species. The model is studied in both theoretical and numerical forms, based on the existence and behavior of the system's steady state. Moreover, it is noticed from the simulation, oxygen depletion can arise if the temperature exceeds a certain critical level. Interestingly, in a certain parameter range, our model shows the formation of spatial patterns that are qualitatively the same to those observed in field observations