Quantifying sudden changes in dynamical systems using symbolic networks

TL;DR

This paper introduces a novel method combining symbolic ordinal analysis and network theory to quantify and detect sudden changes in dynamical systems, including empirical laser data, providing early warning signals.

Contribution

It develops new network-based diagnostics from ordinal analysis to characterize dynamical changes and anticipates abrupt transitions in empirical systems.

Findings

Diagnostics successfully detect changes in logistic, tent, and circle maps.

Method anticipates polarization switchings in semiconductor lasers.

Provides early warning signals for abrupt dynamical transitions.

Abstract

We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every node weights represents the probability of an ordinal patterns (OPs) to appear in the symbolic sequence and each edges weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions.