Fig. 2: Collective oscillations emerge at reduced frequencies from time-delayed synchronization.

The system of N = 90 coupled oscillators, Z, was simulated for 50 s in the presence of white noise, varying only two global parameters: the Global Coupling K (increasing exponentially to better capture the effect of delays) and the conduction speed, which scales the Mean Conduction Delay. a–c To illustrate the effect of the coupling strength in the frequency of synchronization, the collective signal given by \({\sum }_{n=1}^{N}{Z}_{n}\). with N = 90 is reported for three levels of global coupling, keeping the same mean conduction delay of 5 milliseconds. The corresponding power spectra are reported on the right of each plot, and the Kuramoto Order Parameter (KOP) is reported below. For weak coupling (a) the simulated signal exhibits oscillations peaking close to the node’s natural frequency. For intermediate coupling (b), weakly stable synchronization generates transient oscillations at reduced frequencies. For strong coupling (c), global synchronization becomes more stable, and all units are entrained in a collective oscillation at a reduced frequency. For intermediate coupling, fluctuations in the order parameter are indicative of metastability. d–g For each simulation across the parameters explored, we report: (d) the mean of the KOP (referred to as Synchrony); (e) the standard deviation of the KOP (referred to as Metastability⁸⁷); (f) the peak frequency of the simulated collective signal; (g) the synchronization frequency predicted analytically, showing agreement with simulation results for sufficient synchrony.