# Real-time vulnerability of synchronized states

## TL;DR

This paper investigates how the vulnerability of synchronized states in complex electronic networks varies over time, showing that the timing of disturbances critically affects whether synchronization is maintained or lost.

## Contribution

It systematically analyzes the time-dependent vulnerability of synchronized states and introduces a safety index to characterize perturbation effects at different moments.

## Key findings

- Timing of perturbations determines desynchronization or restoration.
- Vulnerability is linked to state space sensitivities along trajectories.
- Complex patterns of stability and instability depend on event timing.

## Abstract

The time-dependent vulnerability of synchronized states is shown for a complex network composed of electronic circuits. We demonstrate that disturbances to the local dynamics of network units can produce different outcomes to synchronization depending on the event timing. We address such time dependence by systematically perturbing the synchronized system at instants of time equally distributed along its trajectory. We find the time instants at which the perturbation desynchronizes the network to be complicatedly mixed with the ones that restore synchronization. Additionally, we characterize perturbation sets obtained for consecutive instants of time by defining a safety index between them. Finally, we demonstrate that the vulnerability is due to state space sensitivities occurring along synchronized trajectories.