Mathematical modeling and analysis of the impact of global warming on the dynamics of polar bear population

Abstract

The last few decades witnessed a continuous decline in the Arctic sea ice cover due to global warming. The change in Arctic ice cover can pose a negative impact on the polar bear (Ursus maritimus) population. This work presents a non-linear model to study the impact of global warming on sea ice cover and the dynamics of the polar bear population. In the model construction, five dynamic variables namely; the Arctic sea ice extent, polar bear population, atmospheric carbon dioxide ( https://www.w3.org/1998/Math/MathML"> CO 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003367420/4193d31d-678d-4cb1-8b03-b46b17bd9b68/content/C007_equ_0001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ) concentration, human population, and mean surface temperature are considered. It is assumed that the increase in https://www.w3.org/1998/Math/MathML"> CO 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003367420/4193d31d-678d-4cb1-8b03-b46b17bd9b68/content/C007_equ_0002.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> level in the atmosphere causes upsurge in the surface temperature which leads to a reduction in ice sheet cover. The reduction in ice sheet cover alters the albedo, which contributes to the further warming of the Earth’s atmosphere. The stability properties of the interior equilibria are examined by using Liapunov direct method. The sensitivity analysis of the model solutions is made to assess the influence of the perturbations in the important model parameter values on the system’s dynamics. It is found that the increase in the anthropogenic https://www.w3.org/1998/Math/MathML"> CO 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003367420/4193d31d-678d-4cb1-8b03-b46b17bd9b68/content/C007_equ_0003.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> emission rate and melting rate of Arctic sea ice cover lead to a decline in the equilibrium level of the polar bear population. Numerical simulation is performed to complement the analytical results.