Extreme variability in convergence to structural balance in frustrated dynamical systems

TL;DR

This paper investigates how fully connected networks of discrete dynamical elements evolve towards structural balance, revealing that stochastic fluctuations cause highly variable convergence times characterized by bimodal distributions.

Contribution

It introduces a model of link adaptation based on Hebb's principle and analyzes the impact of stochastic fluctuations on convergence variability.

Findings

Convergence times exhibit bimodal distribution due to stochastic fluctuations.

Variability in convergence is significant and non-trivial, indicating complex energy landscape dynamics.

The model provides insights into the adaptation process in complex networks.

Abstract

In many complex systems, the dynamical evolution of the different components can result in adaptation of the connections between them. We consider the problem of how a fully connected network of discrete-state dynamical elements which can interact via positive or negative links, approaches structural balance by evolving its links to be consistent with the states of its components. The adaptation process, inspired by Hebb's principle, involves the interaction strengths evolving in accordance with the dynamical states of the elements. We observe that in the presence of stochastic fluctuations in the dynamics of the components, the system can exhibit large dispersion in the time required for converging to the balanced state. This variability is characterized by a bimodal distribution, which points to an intriguing non-trivial problem in the study of evolving energy landscapes.