Modeling the Phenomenon of Xenophobia in Africa
DOI:
https://doi.org/10.5614/j.math.fund.sci.2021.53.2.7Keywords:
Boundedness, Global stability, Local bifurcation, Xenophobes, Xenophobic-mathematical modelAbstract
In this study, we applied the principle of a competitive predator-prey system to propose a prey-predator-like model of xenophobia in Africa. The boundedness of the solution, the existence and stability of equilibrium states of the xenophobic model are discussed accordingly. As a special case, the coexistence state was found to be locally and globally stable based on the parametric conditions of effective group defense and anti-xenophobic policy implementation. The system was further analyzed by Sotomayor?s theory to show that each equilibrium point bifurcates transcritically. However, numerical proof showed period-doubling bifurcation, which makes the xenophobic situation more chaotic in Africa. Further numerical simulations support the analytical results with the view that tolerance, group defense and anti-xenophobic policies are critical parameters for the coexistence of foreigners and xenophobes.
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