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Chimera index and metastability index
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Cognitive chimera states in human brain networks

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We calculated the chimera index, C, and metastability index, λ, as described in (24, 34). C is a measure of the normalized average variation in the order parameter within cognitive systems averaged over time. For si ∈ [s1, s2, …, sM] (M = 9 is the total number of systems)$C=<σch(t)>TCMax$(9)where$σch(t)=1M−1∑i=1M(ρsi(t)−<ρs(t)>M)2$(10)

In this case, CMax = 5/36 is a normalization factor and represents the maximum value of variability in the order parameter in an ideal chimera state where the network organizes such that the half of its population is completely synchronized and half is completely desynchronized (34). The instantaneous quantity <ρs(t)>M measures the synchronization of cognitive systems, averaged over all systems at a given time t.

Similarly, λ measures the normalized temporal variation of the order parameter averaged across all cognitive systems$λ=<σmet(s)>MλMax$(11)where$σmet(s)=1T−1∑t≤T(ρsi(t)−<ρsi>T)2$(12)

Here, λMax = 1/12 is a normalization factor (34), representing the scenario where the system spends equal time in all stages of synchronization.

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