Anomaly, class division, and decoupling in income dynamics

Economic inequality emerges from the interplay between regional growth-rate differences and the interaction network that couples regions. We propose a minimal income-dynamics model, where heterogeneity is governed by growth-rate assortativity $\mathcal{A}$ and regional concentration $\mathcal{R}$, allowing us to quantify the spatiotemporal patterns of empirically observed log-income distributions. To systematically analyze these patterns, we derive closed-form approximations for the Hellinger distance and the Gini index in limiting configurations. Our findings highlight the spatial segregation of growth rates as a key driver of economic class division and demonstrate how small-world shortcuts in the underlying network can disrupt this segregation. Finally, our framework provides a robust explanation for the bimodality and strong regional correlations found in global income distributions.