The human brain's cerebral cortex exhibits a topographic division into higher-order transmodal core and lower-order unimodal periphery regions. While timescales between the core and periphery region diverge, features of their power spectra, especially scale-free dynamics during resting-state and their mdulation in task states, remain unclear. To answer this question, we investigated the ~1/f-like pink noise manifestation of scale-free dynamics in the core-periphery topography during rest and task states applying infra-slow inter-trial intervals up to 1 min falling inside the BOLD's infra-slow frequency band. The results demonstrate (1) higher resting-state power-law exponent (PLE) in the core compared to the periphery region; (2) significant PLE increases in task across the core and periphery regions; and (3) task-related PLE increases likely followed the task's atypically low event rates, namely the task's periodicity (inter-trial interval = 52–60 s; 0.016–0.019 Hz). A computational model and a replication dataset that used similar infra-slow inter-trial intervals provide further support for our main findings. Altogether, the results show that scale-free dynamics differentiate core and periphery regions in the resting-state and mediate task-related effects.
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