Anomalous metapopulation dynamics on scale-free networks

TL;DR

This paper investigates how anomalous residence times in scale-free networks influence individual movement, revealing that weakly connected nodes can dominate in attracting individuals, challenging classical assumptions.

Contribution

It introduces a fractional analysis approach showing that anomalous inertia effects can override the influence of highly connected nodes in network dynamics.

Findings

Residence time distribution has a non-trivial U-shape.

Anomalous inertia effects dominate in attracting individuals.

Empirical evidence from human residence and employment times.

Abstract

We model transport of individuals across a heterogeneous scale-free network where a few weakly connected nodes exhibit heavy-tailed residence times. Using the empirical law Axiom of Cumulative Inertia and fractional analysis we show that `anomalous cumulative inertia' overpowers highly connected nodes in attracting network individuals. This fundamentally challenges the classical result that individuals tend to accumulate in high-order nodes. The derived residence time distribution has a non-trivial U-shape which we encounter empirically across human residence and employment times.