Abstract
This paper presents a strategy for detecting the onset of a critical transition from synchronization to uncorrelated behavior—called here pre-desynchronized state—occurring in networks composed of noisy oscillatory units. In the analysis, we exploit the fact that, at the critical point where the transition takes place, the covariance matrix of the linearized error dynamics becomes unbounded, i.e., at the pre-desynchronized state some of the synchronization errors will exhibit large and slow fluctuations. The critical point is characterized by the dominant eigenvalue of the synchronization error dynamics, which is assumed to be either real or a complex conjugated pair. In the analysis, we consider a generic family of linear non-autonomous oscillators and a network of FitzHug-Nagumo neurons as particular examples.
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