Coherent Dynamics Enhanced by Uncorrelated Noise

Abstract

Synchronization is a widespread phenomenon observed in physical, biological, and social networks, which persists even under the influence of strong noise. Previous research on oscillators subject to common noise has shown that noise can actually facilitate synchronization, as correlations in the dynamics can be inherited from the noise itself. However, in many spatially distributed networks, such as the mammalian circadian system, the noise that different oscillators experience can be effectively uncorrelated. Here, we show that uncorrelated noise can in fact enhance synchronization when the oscillators are coupled. Strikingly, our analysis also shows that uncorrelated noise can be more effective than common noise in enhancing synchronization. We first establish these results theoretically for phase and phase-amplitude oscillators subject to either or both additive and multiplicative noise. We then confirm the predictions through experiments on coupled electrochemical oscillators. Our findings suggest that uncorrelated noise can promote rather than inhibit coherence in natural systems and that the same effect can be harnessed in engineered systems.

Enhancing synchronization by optimal correlated noise

“…Using analytic arguments we find that in the simple case of two coupled oscillators in the phase-drift regime as studied in Ref. [36], the optimal synchrony-enhancing noise undergoes a transition from perfect anti-correlation to perfect correlation as the total noise strength is increased. Making contact with relevant real-world networks such as power grids [9], we then numerically study generic complex networks near phaselocked fixed points and show that the optimal pattern of synchrony-enhancing noise retains the anti-correlation characteristics seen in the two-oscillator case.…”

“…The model described by Eq. ( 1) was recently shown to exhibit counter-intuitive enhanced synchronization under uncorrelated noise C ij ∼ δ ij as opposed to common noise C ij = C [36]. We now study this effect allowing for arbitrary correlations between the noise terms.…”

“…Similar techniques have also been effective for other types of networks and objectives, such as efficient transport [29][30][31][32][33][34][35]. At the same time, there has been recent interest in the possibility that noise may be leveraged to enhance synchronization [36][37][38][39][40][41][42]. Specifically, it was found that the degree to which input noise is correlated may have a significant influence on its ability to aid in or prevent network synchrony [36].…”

“…1 (a), Ref. [36]}. At fixed κ, it becomes clear that there exists an optimal effective noise ς 2 * that maximizes synchronization.…”

“…In summary, we studied to what extent synchronization in complex oscillator networks can be controlled and enhanced by correlated noise. While previous work suggested that uncorrelated noise may improve synchronization in a system of two oscillators [36], here we presented a full analysis of the effect of correlated noise. In the phase-drift regime, where noise can significantly improve synchronization, we analytically found that the optimal degree of correlation between the two noisy inputs depends strongly on the noise strength itself.…”