Cortical oscillations and scale-free neural activity are thought to influence a variety of cognitive functions, but their differential relationships to neural stability and flexibility has never been investigated. Based on the existing literature, we hypothesize that scale-free and oscillatory processes in the brain exhibit different trade-offs between stability and flexibility; specifically, cortical oscillations may reflect variable, task-responsive aspects of brain activity, while scale-free activity is proposed to reflect a more stable and task-unresponsive aspect. We test this hypothesis using data from two large-scale MEG studies (HCP: n = 89; CamCAN: n = 195), operationalizing stability and flexibility by task-responsiveness and spontaneous intra-subject variability in resting state. We demonstrate that the power-law exponent of scale-free activity is a highly stable parameter, which responds little to external cognitive demands and shows minimal spontaneous fluctuations over time. In contrast, oscillatory power, particularly in the alpha range (8–13 Hz), responds strongly to tasks and exhibits comparatively large spontaneous fluctuations over time. In sum, our data support differential roles for oscillatory and scale-free activity in the brain with respect to neural stability and flexibility. This result carries implications for criticality-based theories of scale-free activity, state-trait models of variability, and homeostatic views of the brain with regulated variables vs. effectors.
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