Large order fluctuations, switching, and control in complex networks

TL;DR

This paper introduces an analytical method to study large fluctuations and switching behavior in complex networks, revealing how network structure influences transition probabilities and times.

Contribution

It develops a novel analytical framework for quantifying large fluctuations and switching times in complex networks, incorporating network heterogeneity effects.

Findings

Probability of large fluctuations decreases exponentially with participation ratio.

Network heterogeneity significantly influences fluctuation scaling patterns.

Optimal targeting strategies can be identified to control switching times.

Abstract

We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of fluctuations from one ordered state to another in real and synthetic networks. The method allows us to compute the distribution of large fluctuations and the time scale associated with switching between ordered states for networks consistent with mean-field assumptions. In general, we quantify how network heterogeneity influences the scaling patterns and probabilities of fluctuations. For instance, we find that the probability of a large fluctuation near an order-disorder transition decreases exponentially with the participation ratio of a network's principle eigenvector -- measuring how many nodes effectively contribute to an ordered state. Finally, the proposed theory is used to answer how and where a network should be targeted in order to optimize the time needed to observe a switch.