# Quantifying information loss on chaotic attractors through recurrence networks

## TL;DR

This paper introduces an entropy measure based on recurrence networks to analyze chaotic attractors, effectively distinguishing chaos from noise and quantifying information loss due to structural changes.

## Contribution

The paper presents a novel entropy measure derived from recurrence networks that converges with data size and captures structural differences in chaotic attractors.

## Key findings

- The measure converges to a constant with increasing data points and embedding dimension.
- It effectively distinguishes chaotic attractors from white noise.
- It quantifies information loss via link density differences in recurrence networks.

## Abstract

We propose an entropy measure for the analysis of chaotic attractors through recurrence networks which are un-weighted and un-directed complex networks constructed from time series of dynamical systems using specific criteria. We show that the proposed measure converges to a constant value with increase in the number of data points on the attractor (or the number of nodes on the network) and the embedding dimension used for the construction of the network, and clearly distinguishes between the recurrence network from chaotic time series and white noise. Since the measure is characteristic to the network topology, it can be used to quantify the information loss associated with the structural change of a chaotic attractor in terms of the difference in the link density of the corresponding recurrence networks. We also indicate some practical applications of the proposed measure in the recurrence analysis of chaotic attractors as well as the relevance of the proposed measure in the context of the general theory of complex networks.