Reply to Comment on "Synchronization dynamics in non-normal networks: the trade-off for optimality"

TL;DR

This paper defends the original findings on synchronization in non-normal networks against a comment, clarifying misunderstandings and providing additional evidence that optimal networks can be fragile to perturbations.

Contribution

It clarifies the validity of previous results on synchronization dynamics and counters claims that challenge the robustness of optimal networks.

Findings

Optimal networks' synchronized states are fragile to perturbations.

The comment's interpretation of optimality is subjective and not aligned with the original framework.

Additional literature supports the original conclusion about fragility.

Abstract

We reply to the recent note "Comment on Synchronization dynamics in non-normal networks: the trade-off for optimality", showing that the authors base their claims mainly on general theoretical arguments that do not necessarily invalidate the adequacy of our previous study. In particular, they do not specifically tackle the correctness of our analysis but instead limit their discussion on the interpretation of our results and conclusions, particularly related to the concept of optimality of network structure related to synchronization dynamics. Nevertheless, their idea of optimal networks is strongly biased towards their previous work and does not necessarily correspond to our framework, making their interpretation subjective and not consistent. We bring here further evidence from the existing and more recent literature, omitted in the Comment note, that the synchronized state of oscillators coupled through optimal networks, as intended by the authors, can indeed be highly fragile to small but finite perturbations, confirming our original results.