Early Warning Signals of Oxygen-Plankton Dynamics: Mathematical Approach

Abstract

Any significant decrease in net oxygen production by phytoplankton is likely to result in the loss of atmospheric oxygen and the global extinction of living beings owing to more than half of the atmospheric oxygen provided by marine phytoplankton. The rate of oxygen production is known to depend on water temperature and hence can therefore be affected by global warming.  In this work, it is assumed that oxygen production varies with time under the effect of increasing temperature.  This ecological problem is addressed  theoretically by a couple of plankton-oxygen dynamics. A nonlinear mathematical model is considered to investigate the effect of temperature on oxygen-plankton dynamics. The model is analysed analytical and numerical ways, based on the behavior and complexity of the system's steady state. From the analysis of the model, it has been observed that as temperature level goes above the critical threshold of oxygen production rate  the equilibrium density of plankton population decrease due to a decrease in oxygen concentration. It has also been shown that the system can exhibit sustainable dynamics that can still lead to an environmental disaster, i.e. oxygen depletion and plankton extinction. In this case, extinction takes place after a considerable length  of time.

Keywords

• Global warming,differential equation,extinction,oxygen depletion

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