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Broadband Criticality of Human Brain Network Synchronization

Figure 3

Simulated Kuramoto model data.

Top row: results from system at critical coupling strength , bottom row: no coupling, i.e. free running oscillators. In all panels simulation data is denoted by solid lines (filled symbols) and the corresponding surrogate data by dotted lines. The colors encode wavelet scales 3–11. Left column: Power spectrum of simulated Kuramoto model time series plotted on logarithmic axes. In the critical state the spectrum shows clustering of the effective frequencies forming a common broad peak and follows a power law with exponent −2 on the low-frequency end. The spectrum of the uncoupled model is a simple superposition of the natural oscillator frequencies. The colored vertical lines represent the frequency intervals corresponding to wavelet scales 3–11 (scales 1 and 2 indicated by dotted lines not used). Middle column: Probability distributions for phase-lock interval PLI. Only the critical system produces a power law, clearly distinct from the surrogate data showing an exponential fall-off. The black dashed line represents a power law with . Right column: Probability distribution for lability of global synchronization is plotted on logarithmic axes for each wavelet scale. Again a power law is only seen in the critical model, whereas surrogate data and uncoupled model produce exponential distributions. The straight dashed line represents a power law with .

Figure 3