Self-Organization in Networks: A Data-Driven Koopman Approach

TL;DR

This paper introduces a data-driven Koopman spectrum method to analyze local patterns and regime shifts in network dynamics, specifically focusing on synchronization and self-organized criticality.

Contribution

It presents a novel Koopman spectrum approach for studying regime shifts in network dynamics, demonstrated on oscillator synchronization and SOC models.

Findings

Identifies local patterns near regime shifts in network dynamics.

Analyzes synchronized behavior in IFO systems.

Examines SOC phenomena in Bak-Sneppen model.

Abstract

Networks out of equilibrium display dynamics characterized by multiple equilibria and sudden transitions. These transitions arise when each node leaves its natural stable state and joins to an organized global activation behavior. In this paper, we study local patterns near regime shifts in Network Synchronization and Self-Organized Criticality (SOC) by a Koopman spectrum data-driven approach. To illustrate these ideas, we use synchronized behavior from an Integral-and-Fire oscillators (IFO) system and SOC in the Bak-Sneppen model.