Network Mutual Information and Synchronization under Time Transformations

TL;DR

This paper studies how general time transformations affect phase synchronization and mutual information in dynamical networks, showing invariance properties and implications for communication.

Contribution

It demonstrates the invariance of phase synchronization and mutual information rate under time transformations and explores their impact on network communication.

Findings

PS cannot be created or destroyed by time transformations

MIR cannot increase from zero through time transformations

Proper time transformations can improve cycle timing in coupled oscillators

Abstract

We investigate the effect of general time transformations on the phase synchronization (PS) phenomenon and the mutual information rate (MIR) between pairs of nodes in dynamical networks. We demonstrate two important results concerning the invariance of both PS and the MIR. Under time transformations PS can neither be introduced nor destroyed and the MIR cannot be raised from zero. On the other hand, for proper time transformations the timing between the cycles of the coupled oscillators can be largely improved. Finally, we discuss the relevance of our findings for communication in dynamical networks.