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Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations
Open accessAbstract
The human brain spontaneously generates neural oscillations with a large variability in frequency, amplitude, duration, and recurrence. Little, however, is known about the long-term spatiotemporal structure of the complex patterns of ongoing activity. A central unresolved issue is whether fluctuations in oscillatory activity reflect a memory of the dynamics of the system for more than a few seconds. We investigated the temporal correlations of network oscillations in the normal human brain at time scales ranging from a few seconds to several minutes. Ongoing activity during eyes-open and eyes-closed conditions was recorded with simultaneous magnetoencephalography and electroencephalography. Here we show that amplitude fluctuations of 10 and 20 Hz oscillations are correlated over thousands of oscillation cycles. Our analyses also indicated that these amplitude fluctuations obey power-law scaling behavior. The scaling exponents were highly invariant across subjects. We propose that the large variability, the long-range correlations, and the power-law scaling behavior of spontaneous oscillations find a unifying explanation within the theory of self-organized criticality, which offers a general mechanism for the emergence of correlations and complex dynamics in stochastic multiunit systems. The demonstrated scaling laws pose novel quantitative constraints on computational models of network oscillations. We argue that critical-state dynamics of spontaneous oscillations may lend neural networks capable of quick reorganization during processing demands.
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“The power spectra of neural signals typically follow a power-law form (), indicating temporal correlations that persist across multiple timescales (He et al. 2010; Miller et al. 2009; Linkenkaer-Hansen et al. 2001; Touboul and Destexhe 2010).”
From The myth of the Bayesian brain (2025) · cites this paper as Linkenkaer-Hansen et al. 2001
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Liu, L., & Hu, F. (2014) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/105/40006 · Cited by 3
Prosthetic Motor Imaginary Task Classification Using Single Channel of Electroencephalography
Haggag, S., Mohamed, S. M. K., Haggag, H., & Nahavandi, S. (2015) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/smc.2015.176 · Cited by 3
“The most famous method for recording human’s brain behavior is EEG [15], the reason behind that is that EEG is a very safe, simple and non-invasive procedure.”
MethodGestalt Phenomenon in Music: Which Frequencies Do We Really Hear?
Ghosh, D. C., Sengupta, R., Sanyal, S., & Banerjee, A. (2017) · Signals and communication technology · doi:10.1007/978-981-10-6511-8_7 · Cited by 3
The role of noise modeling in the estimation of resting-state brain effective connectivity
Prando, G., Zorzi, M., Bertoldo, A., & Chiuso, A. (2018) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2018.09.206 · Cited by 3
Evaluation of Musical Quality of Tanpura by Non Linear Analysis
Datta, A. K., Sengupta, R., Banerjee, K., & Ghosh, D. C. (2018) · Signals and communication technology · doi:10.1007/978-981-13-2610-3_9 · Cited by 3
A memory-based method to select the number of relevant components in principal component analysis
Verma, A., Vivo, P., & Matteo, T. D. (2019) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ab3bc4 · Cited by 3
“[37] Klaus Linkenkaer-Hansen, Vadim V Nikouline, J Matias Palva, and Risto J Ilmoniemi.”
BackgroundFractal brain dynamics: from Mandelbrot to marmosets
Roisen, D. A., & Shew, W. L. (2020) · The Journal of Physiology · doi:10.1113/jp279556 · Cited by 3
“In fact, similar to the analysis done by Munn et al. much of the evidence for the criticality hypothesis in humans is based on fractal structure of temporal fluctuations in EEG or MEG (Linkenkaer-Hansen et al. 2001).”
BackgroundResultInfluentialCritical Neural Networks Minimize Metabolic Cost
Aguilar-Velázquez, D. (2021) · Physics · doi:10.3390/physics3010005 · Cited by 4
“Moreover, SOC systems are strongly related to long-range time correlations (1/ f noise [5]) and fractal fluctuations [6], indicating dynamic processes with memory, which is found in real neural networks [7].”
BackgroundGolemme, M., Tatti, E., Luft, C. D. B., Bhattacharya, J., Ruiz, M. H., & Cappelletti, M. (2021) · European Journal of Neuroscience · doi:10.1111/ejn.15486 · Cited by 4
“…20 non-overlapping windows of equal size T in the logarithmic scale; these ranged from 1 to 18 seconds, with the maximum window (18 seconds) being 1/10 of the total length (i.e. 180 seconds), as recommended in the previous studies (Herrojo Ruiz et al., 2014; Klaus Linkenkaer-Hansen et al., 2001).”
Huo, Y., Zhao, G., Ruan, L., Xu, P., Fang, G., Zhang, F., Bao, Z., & Li, X. (2022) · BMC Bioinformatics · doi:10.1186/s12859-021-04286-2 · Cited by 5
“Studies of human brain oscillations [3], computer network traffic and the Internet [4, 5], financial markets [6], forest fires [7], ecosystems [8, 9], climate systems [10, 11], economics and global finance [12], neuronal networks [13], and biological macroevolution have all revealed such critical dynamics [14].”
BackgroundThe Neuronal Network Oscillation as a Critical Phenomenon
Hardstone, R., Mansvelder, H. D., & Linkenkaer‐Hansen, K. (2014) · Wiley eBooks · doi:10.1002/9783527651009.ch13 · Cited by 3
Self-citationAVALANCHE CORRELATION IN POWER SPECTRA WITH WIDE PEAKS
Eggenhöffner, R., Celasco, E., & Celasco, M. (2007) · Fluctuation and Noise Letters · doi:10.1142/s0219477507003994 · Cited by 3
Distinct criticality of phase and amplitude dynamics in the resting brainPreprint
Ton, R., Deco, G., Kringelbach, M. L., Woolrich, M. W., & Daffertshofer, A. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1512.02574 · Cited by 3
“Spectral distributions of encephalographic signals have 1 = f -structures (Freeman and van Dijk, 1987; Dehghani et al., 2010; He et al., 2010; Fransson et al., 2013; Lei et al., 2015) and their auto-correlation structures also show power-law behavior (Linkenkaer-Hansen et al., 2001, 2007).”
BackgroundResultInfluentialPower-law dynamics in cortical excitability as probed by early somatosensory evoked responses
Stephani, T., Waterstraat, G., Haufe, S., Curio, G., Villringer, A., & Nikulin, V. V. (2019) · MPG.PuRe (Max Planck Society) · Cited by 3
Haque, H., Hirvonen, J., Wang, S. H., Simola, J., Morales‐Muñoz, I., Cowley, B. U., Palva, J. M., & Palva, S. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.12.14.519751 · Cited by 3
Self-citationHierarchical whole-brain modeling of critical synchronization dynamics in human brainPreprint
Myrov, V. O., Suleimanova, A., Knapič, S., Partanen, P., Vesterinen, M., Liu, W., Palva, S., & Palva, J. M. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.05.08.593146 · Cited by 3
“…a hierarchical implementation of the Kuramoto model to the whole-brain scale, we found here how simultaneous modeling of local and inter-areal synchronization dynamics reveals a multi-scale transition from an asynchronous to a synchronized phase in both node order and inter-areal phase synchrony.”
InfluentialSelf-citationThe Hurst exponent as a marker of inhibition in the developing brainPreprint
Nishio, M., Ellwood-Lowe, M. E., Woodburn, M., McDermott, C. L., Park, A. T., Tooley, U. A., Boroshok, A. L., Grandjean, J., & Mackey, A. P. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.09.29.615675 · Cited by 3
Cochrane, A., Rosedahl, L. A., Tamaki, M., Watanabe, T., & Sasaki, Y. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.03.31.646339 · Cited by 3
Is critical brain dynamics more prevalent than previously thought?Preprint
Fontenele, A. J., Sooter, J. S., Ziarati, E., Barreiro, A. K., Ly, C., & Shew, W. L. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.09.02.673722 · Cited by 3
“The third property is motivated by traditional LRTC analysis, which is based on DFA analysis of the power envelope of a chosen frequency band [8–10].”
InfluentialCROCOpy - A Python toolbox for the analysis of CRitical Oscillations and COnnectivityPreprint
Myrov, V. O., Siebenhühner, F., Wang, S. H., Arnulfo, G., Juvonen, J. J., Roascio, M., Burlando, G., Suleimanova, A., Repo, J., Liu, W., et al. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.02.17.706438 · Cited by 3
“It can be assessed with detrended fluctuation analysis (DFA; Linkenkaer-Hansen et al., 2001).”
Self-citationSong, H., Cui, J., Hu, G., Xiong, L., Wutthinitikornkit, Y., Lei, H., & Li, J. (2025) · Advanced Science · doi:10.1002/advs.202412989 · Cited by 2
Neuronal oscillatory imbalances in GNAO1 ‐related disorders associated with disease severity
Wang, T., Domínguez‐Carral, J., Ludlam, W. G., Segarra, M. J., Marti, M. F., Bruining, H., Martemyanov, K. A., Linkenkaer‐Hansen, K., & Ortigoza‐Escobar, J. D. (2025) · Epilepsia · doi:10.1111/epi.18513 · Cited by 2
“14,15 First, we obtain the amplitude envelope by taking the absolute value of the Hilbert transform.”
Self-citationKuc, A. K. (2025) · Scientific School Dynamics of Complex Networks and their Applications (DCNA) · doi:10.1109/dcna67486.2025.11199953 · Cited by 2
Miles, J. T., Weaver, K. E., Webb, S. J., & Ojemann, J. G. (2025) · Journal of Neurophysiology · doi:10.1152/jn.00435.2025 · Cited by 2
Nonlinear dynamics and multiscale mechanisms of deep brain stimulation
Yuan, Y., Hao, Y., Zhang, K., Guo, Z., & Wang, Z. (2026) · Frontiers in Neuroscience · doi:10.3389/fnins.2026.1778894 · Cited by 2
Slow wave generation and propagation in a model of brain lesions
Gaglioti, G., Porta, L. D., Colombo, M. A., Russo, S., Nieus, T. R., Deco, G., Corbetta, M., Sarasso, S., Sanchez-Vives, M. V., & Massimini, M. (2026) · NeuroImage · doi:10.1016/j.neuroimage.2026.121817 · Cited by 2
Qualitative EEG abnormalities in ASD reflect inhibition-dominated brain dynamics
Avrămiea, A.-E., Juárez-Martinez, E. L., Garcés, P., Hipp, J. F., Poil, S., Diachenko, M., Mansvelder, H. D., Jones, E., Mason, L., Murphy, D., et al. (2026) · Scientific Reports · doi:10.1038/s41598-026-42120-y · Cited by 2
“The analytical steps for the algorithm are as follows: to test the relationship between the amplitude and LRTC of the amplitude envelope of an oscillatory signal, it is necessary to have a measure of LRTC on short time-scales that is unbiased by the amplitude of the signal.”
InfluentialSelf-citationTerrier, P. (2026) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2026.131842 · Cited by 2
Metadata
- Authors
- Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J.
- Affiliations
- Helsinki University Hospital (FI)
- University of Helsinki (FI)
- Venue
- The Journal of Neuroscience
- Publisher
- Society for Neuroscience
- Published
- 2001-02-15
- Volume
- 21
- Issue
- 4
- Pages
- 1370-1377
- ISSN
- 0270-6474 (ISSN-L)
- 1529-2401
- PMC
- PMC6762238
- OpenAlex
- W2139852582
- Cited by
- 1,149
- References
- 50
- Citations by year
- 2026: 63 · 2025: 70 · 2024: 63 · 2023: 53 · 2022: 76 · 2021: 60 · 2020: 63 · 2019: 57 · 2018: 65 · 2017: 66 · 2016: 62 · 2015: 43 · 2014: 53 · 2013: 48 · 2012: 45
- FWCI
- 6.12
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of Neuroscience (publishedVersion, cc-by-nc-sa)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Funders
- Helsingin ja Uudenmaan Sairaanhoitopiiri
- Academy of Finland
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Keywords
- long-range temporal correlations, power-law scaling, neural oscillations, spontaneous neuronal activity, self-organized criticality, neural network reorganization, scaling exponents
- MeSH terms
- Adult, Biological Clocks, Brain, Computer Simulation, Electroencephalography, Female, Humans, Male, Models, Neurological, Nerve Net, Occipital Lobe, Parietal Lobe, Signal Processing, Computer-Assisted, Stochastic Processes, Time Factors, Visual Perception, Magnetoencephalography, Fractals
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