Time-Scale and Noise Optimality in Self-Organized Critical Adaptive Networks

TL;DR

This paper investigates how adaptive networks self-organize into critical states, revealing that optimal noise and time-scale separation occur at finite values, contrary to previous beliefs, and identifies a noise-induced phase transition.

Contribution

It demonstrates that noise and time-scale optimality in self-organized critical networks occur at finite values and uncovers a noise-induced phase transition, challenging prior assumptions.

Findings

Optimal noise and time-scale separation occur at finite values.

Discovered a noise-induced phase transition in SOC.

Identified three low-dimensional dynamical behaviors: TR, SSR, and phase transitions.

Abstract

Recent studies have shown that adaptive networks driven by simple local rules can organize into "critical" global steady states, providing another framework for self-organized criticality (SOC). We focus on the important convergence to criticality and show that noise and time-scale optimality are reached at finite values. This is in sharp contrast to the previously believed optimal zero noise and infinite time scale separation case. Furthermore, we discover a noise induced phase transition for the breakdown of SOC. We also investigate each of the three new effects separately by developing models. These models reveal three generically low-dimensional dynamical behaviors: time-scale resonance (TR), a new simplified version of stochastic resonance - which we call steady state stochastic resonance (SSR) - as well as noise-induced phase transitions.