A nonautonomous mathematical model to assess the impact of algae on the abatement of atmospheric carbon dioxide

Abstract

The world’s oceans have played an important role in sequestering atmospheric carbon dioxide through solubility and the action of algae. Fixation of atmospheric carbon dioxide by photoautotrophic algal cultures has the potential to diminish the release of carbon dioxide into the atmosphere, thereby helping to alleviate the trend toward global warming. This work investigates the role of algae in controlling the level of atmospheric carbon dioxide. Partial Rank Correlation Coefficients (PRCCs) technique is used to address how the concentration of atmospheric carbon dioxide is affected by changes in a specific parameter disregarding the uncertainty over the rest of the model parameters. Parameters related to algal growth are shown to significantly reduce the level of atmospheric CO2. Further, we explore the dynamics of nonautonomous system by incorporating the seasonal variations of some ecologically important model parameters. Our nonautonomous system exhibits globally attractive positive periodic solution, and also the appearance of double periodic solution is observed. Moreover, by letting the seasonally forced parameters as almost periodic functions of time, we show almost periodic behavior of the system. Our findings suggest that the policy makers should focus on continuous addition of nutrients in the ocean to accelerate the algal growth thereby reducing the level of carbon dioxide in the atmosphere.