Revealing dynamics, communities and criticality from data

TL;DR

This paper introduces a method to predict critical transitions in complex networks by modeling their dynamics through an effective network that captures local chaos and interactions, emphasizing the importance of fluctuations.

Contribution

It presents a novel approach to forecast critical changes in complex systems with chaotic local dynamics by using an effective network model that incorporates fluctuations.

Findings

Behavior decomposes into deterministic and fluctuation components

Fluctuations are crucial for understanding network interactions

Effective network model predicts critical transitions

Abstract

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behaviour for parameter ranges for which no data on the system is available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an {\em effective network}, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behaviour of such networks can be decomposed in terms of an emergent deterministic component and a {\em fluctuation} term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure.