Human cortex organizes dynamic co-fluctuations along the sensorimotor-association axis

Human functional brain networks, originating from coherent fluctuations in brain activity, are organized along a hierarchical axis. However, how this stable hierarchical architecture emerges from time-varying co-fluctuations remains unknown. Existing dynamic analyses have primarily focused on high-amplitude co-fluctuations, largely overlooking the contribution of lower-amplitude activity. Here, we investigated the amplitude-dependent configurations of regional co-fluctuation. We found that these patterns were hierarchically aligned with the sensorimotor-association (SA) axis: sensorimotor networks are preferentially expressed during high-amplitude co-fluctuations, associative systems prevailed during intermediate amplitudes, and limbic system preferentially engaged in low-amplitude states. This amplitude-stratified hierarchy underwent developmental refinement from childhood to adulthood and adaptively reconfigured under naturalistic stimuli. Replicated across four independent datasets including 7 T fMRI, these findings uncover a fundamental principle whereby the brain's hierarchical architecture is actively preserved through a structured, amplitude-dependent cascade of functional co-fluctuations. Our framework bridges dynamic coordination and stable architecture, demonstrating how the brain balances external processing with internal cognition through amplitude-stratified interactions.