Analisis Kestabilan Model Matematika Predator-Prey pada Dinamika Sosial

Abstract

In social life, difference and diversity is something that cannot be denied by anyone. Starting from differences horizontally concerning ethnicity, language, customs to religion and vertically concerning the political, social, cultural to economic fields. The existence of these many differences can certainly bring positive and negative impacts in social life. With diversity, interaction in society is dynamic, but it results in the emergence of negative attitudes such as egoism and competition between groups. From the occurrence of this can trigger the problem of social inequality in the community. Social inequality can occur because of national development efforts that only focus on economic aspects and forget about social aspects. The purpose of this thesis is to discuss the stability analysis of the predator-prey mathematical model on social dynamics with the Holling type II functional response. From this model analysis, we obtained four equilibrium points, which are the equilibrium point for the extinction of all population (E0) which is unstable, then the equilibrium point for the extinction of the non-poor population and the poor (E1) and the extinction of the non-poor population (E2) which are stable with certain conditions and coexistence (E3) which is to be asymptotically stable. Also in the final section, we perform the numerical simulation to supports the analytical result.