Modeling the Phenomenon of Xenophobia in Africa

Abstract

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.

Keywords

• Boundedness
• Global stability
• Local bifurcation
• Xenophobes
• Xenophobic-mathematical model