Inequalities in Cooperative Generalized Lotka-Volterra model with Random Regular Graph Structure

Abstract

The Generalized Lotka-Volterra (GLV) model, widely employed in population dynamics, serves to characterize how interactions between species influence system equilibria. This model can be extended to the economic domain to quantify wealth inequality among individuals. In this thesis, we explore the impact of the underlying random network structure on the final distribution of abundances, with a focus on homogeneous degree settings, particularly regular random graphs. While the GLV model has been extensively studied in competitive and predator-prey scenarios, the mutualistic (or cooperative) case has received less attention due to the divergence of species abundances. In the context of this divergence, we investigate the hierarchy of infinities by revisiting the GLV model and introducing a framework wherein species undergo relative extinction when compared to others. For large interaction strengths, we observe the emergence of effective competition within a cooperative system, resulting in localization, a phenomenon in which a few highly connected species dominate and accumulate most of the wealth. As interaction strength decreases, the surviving component follows a geometrical evolution, which we analytically quantify in this work. Finally, we discuss the implications of this framework for wealth inequality through the Gini index and extend the analysis to heterogeneous degree settings using the Erdos-Renyi random graph mode