A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain’s hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
A new inter-disciplinary relationship: introducing self-organized criticality to failures in aviation security
Journal of Transportation Security Open Access 16 November 2023
Scientific Reports Open Access 31 July 2023
Nature Communications Open Access 03 May 2023
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Bak, P. How Nature Works (Oxford Univ. Press, 1997).
Jensen, H. J. Self-Organized Criticality (Cambridge Univ. Press, 1998).
Buchanan, M. Ubiquity (Weidenfeld and Nicolson, 2000).
Christensen, K. & Moloney, N. R. Complexity and Criticality (Imperial College Press, 2005).
Aldana, M., Balleza, E., Kauffman, S. A. & Resendis, O. Robustness and evolvability in genetic regulatory networks. J. Theor. Biol. 245, 433–448 (2007).
Balleza, E. et al. Critical dynamics in genetic regulatory networks: Examples from four kingdoms. PLoS ONE 3, e2456 (2008).
Lux, T. & Marchesi, M. Scaling and criticality in a stochastic multi-agent model of a financial market. Nature 397, 498–500 (1999).
Malamud, B. D., Morein, G. & Turcotte, D. L. Forest fires: An example of self-organized critical behaviour. Science 281, 1840–1842 (1998).
Nykter, M. et al. Gene expression dynamics in the macrophage exhibit criticality. Proc. Natl Acad. Sci. USA 105, 1897–1900 (2008).
Takayasu, M., Takayasu, H. & Fukuda, K. Dynamic phase transition observed in the internet traffic flow. Physica A 277, 248–255 (2000).
Peters, O. & Neelin, D. Critical phenomena in atmospheric precipitation. Nature Phys. 2, 393–396 (2006).
Peters, O., Hertlein, C. & Christensen, K. A complexity view of rainfall. Phys. Rev. Lett. 88, 018701 (2002).
Peters, O. & Christensen, K. Rain: Relaxations in the sky. Phys. Rev. E 66, 036120 (2002).
Hopfield, J. J. Neural networks and physical systems with emergent collective computational capabilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).
Bak, P. & Paczuski, M. Complexity, contingency, and criticality. Proc. Natl Acad. Sci. USA 92, 6689–6696 (1995).
Anderson, P. More is different. Science 177, 393–396 (1972).
Buzsaki, G. Rhythms of the Brain (Oxford Univ., 2006).
Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M. & Ilmoniemi, R. J. Long-range temporal correlations and scaling behaviour in human brain oscillations. J. Neurosci. 21, 1370–1377 (2001).
Stam, C. J. & de Bruin, E. A. Scale-free dynamics of global functional connectivity in the human brain. Hum. Brain Mapp. 22, 97–109 (2004).
Plenz, D. & Thiagarajan, T. C. The organizing principles of neuronal avalanches: Cell assemblies in the cortex? Trends Neurosci. 30, 101–110 (2007).
Bullock, T. H., Mcclune, M. C. & Enright, J. T. Are the electroencephalograms mainly rhythmic? Assessment of periodicity in wide-band time series. Neuroscience 121, 233–252 (2003).
Logothetis, N. K. The neural basis of the blood-oxygen-level-dependent functional magnetic resonance imaging signal. Phil. Trans. R. Soc. Lond. B 357, 1003–1037 (2002).
Eckhorn, R. Oscillatory and non-oscillatory synchronizations in the visual cortex and their possible roles in associations of visual features. Prog. Brain Res. 102, 405–426 (1994).
Miller, K. J., Sorensen, L. B., Ojemann, J. G. & den Nijs, M. Power law scaling in the brain surface electric potential. PLoS Comput. Biol. 5, e1000609 (2009).
Manning, J. R., Jacobs, J., Fried, I. & Kahana, M. J. Broadband shifts in local field potential power spectra are correlated with single-neuron spiking in humans. J. Neurosci. 29, 13613–13620 (2009).
Gilden, D. L. Cognitive emissions of 1/f noise. Psychol. Rev. 108, 33–56 (2001).
Maylor, E. A., Chater, N. & Brown, G. D. Scale invariance in the retrieval of retrospective and prospective memories. Psychon. Bull. Rev. 8, 162–167 (2001).
Ward, L. M. Dynamical Cognitive Science (The MIT Press, 2002).
Nakamura, T. et al. Universal scaling law in human behavioral organization. Phys. Rev. Lett. 99, 138103 (2007).
Anteneodo, C. & Chialvo, D. R. Unraveling the fluctuations of animal motor activity. Chaos 19, 033123 (2009).
Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987).
Beckers, R., Deneubourg, J-L., Goss, S. & Pasteels, J. M. Collective decision making through food recruitment. Insectes Soc. 37, 258–267 (1990).
Beekman, M. & Sumpter, D. J. T. Ratnieks FLW phase transition between disordered and ordered foraging in pharaohs ants. Proc. Natl Acad. Sci. USA 98, 9703–9706 (2001).
Rauch, E. M., Chialvo, D. R. & Millonas, M. M. Pattern formation and functionality in swarm models. Phys. Lett. A 207, 185–193 (1995).
Nicolis, G. & Prigogine, I. Self-Organization in Nonequilibrium systems: From Dissipative Structures to Order Through Fluctuations (Wiley, 1977).
Cavagna, A. et al. Scale-free correlations in starling flocks. Proc. Natl Acad. Sci. USA 107, 11865–11870 (2010).
Bak, P. & Chialvo, D. R. Adaptive learning by extremal dynamics and negative feedback. Phys. Rev. E 63, 031912 (2001).
Chialvo, D. R. & Bak, P. Learning from mistakes. Neuroscience 90, 1137–1148 (1999).
Beggs, J. M. & Plenz, D. Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003).
Beggs, J. M. & Plenz, D. Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216–5229 (2004).
Zapperi, S., Baekgaard, L. K. & Stanley, H. E. Self-organized branching processes: meanfield theory for avalanches. Phys. Rev. Lett. 75, 4071–4074 (1995).
Eurich, C. W., Herrmann, J. M. & Ernst, U. A. Finite-size effects of avalanche dynamics. Phys. Rev. E 66, 066137 (2002).
Teramae, J. N. & Fukai, T. Local cortical circuit model inferred from power-law distributed neuronal avalanches. J. Comput. Neurosci. 22, 301–312 (2007).
Mazzoni, A. et al. On the dynamics of the spontaneous activity in neuronal networks. PLoS ONE 2, e439 (2007).
Pasquale, V., Massobrio, P., Bologna, L. L., Chiappalone, M. & Martinoia, S. Self-organization and neuronal avalanches in networks of dissociated cortical neurons. Neuroscience 153, 1354–1369 (2008).
Petermann, T. et al. Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proc. Natl Acad. Sci. USA 106, 15921–15926 (2009).
Hahn, G. et al. Neuronal avalanches in spontaneous activity in vivo. J. Neurophysiol. (2010, in the press).
Stewart, C. V. & Plenz, D. Inverted U profile of dopamine-NMDA mediated spontaneous avalanche recurrence in superficial layers o rat prefrontal cortex. J. Neurosci. 23, 8148–8159 (2006).
Gireesh, E. D. & Plenz, D. Neuronal avalanches organize as nested theta- and beta/gamma oscillations during development of cortical layer 2/3. Proc. Natl Acad. Sci. USA 105, 7576–7581 (2008).
Bedard, C., Kroger, H. & Destexhe, A. Does the 1/f frequency scaling of brain signals reflect self-organized critical states? Phys. Rev. Lett. 97, 118102 (2006).
Touboul, J. & Destexhe, A. Can power-law scaling and neuronal avalanches arise from stochastic dynamics? PLoS One 5, e8982 (2010).
Plenz, D. & Chialvo, D. R. Scaling properties of neuronal avalanches are consistent with critical dynamics. Preprint at http://arxiv.org/abs/0912.5369v1 [q-bio.NC] (2009).
Kelso, J. A. S. et al. Phase transition in brain and human behaviour. Phys. Lett. A 169, 134–144 (1992).
Kelso, J. A. S. Phase transitions and critical behaviour in human bimanual coordination. Am. J. Physiol. Regul. Integr. Comp. 15, R1000–R1004 (1984).
Werner, G. Fractals in the nervous system: Conceptual implications for theoretical neuroscience. Front. Physio. 1, 15 (2010).
Bullmore, E. & Sporn, O. Complex brain networks: Graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198 (2009).
Sporns, O., Chialvo, D. R., Kaiser, M. & Hilgetag, C. C. Organization, development and function of complex brain networks. Trends Cog. Sci. 8, 418–425 (2004).
Fox, M. D. & Raichle, M. E. Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nat. Rev. Neurosci. 8, 700–711 (2007).
Smith, S. M. et al. Correspondence of the brains functional architecture during activation and rest. Proc. Natl Acad. Sci. USA 106, 13040–13045 (2009).
Xiong, J., Parsons, L., Gao, J. & Fox, P. Interregional connectivity to primary motor cortex revealed using MRI resting state images. Hum. Brain Mapp. 8, 151–156 (1999).
Cordes, D. et al. Mapping functionally related regions of brain with functional connectivity MR imaging. Am. J. Neuroradiol. 21, 1636–1644 (2000).
Beckmann, C. F., De Luca, M., Devlin, J. T. & Smith, S. M. Investigations into resting-state connectivity using independent component analysis. Phil. Trans. R. Soc. Lond. 360, 1001–1013 (2005).
Fukunaga, M. et al. Large-amplitude, spatially correlated fluctuations in BOLD fMRI signals during extended rest and early sleep stages. Magn. Reson. Imaging 24, 979–992 (2006).
Vincent, J. L. et al. Intrinsic functional architecture in the anaesthetized monkey brain. Nature 447, 83–87 (2007).
Kitzbichler, M. G., Smith, M. L., Christensen, S. R. & Bullmore, E. Broadband criticality of human brain network synchronization. PLoS Comput. Biol. 5, e1000314 (2009).
Kuramoto, Y. Chemical Oscillations, Waves and Turbulence (Springer, 1984).
Fraiman, D., Balenzuela, P., Foss, J. & Chialvo, D. R. Ising-like dynamics in large-scale functional brain networks. Phys. Rev. E 79, 061922 (2009).
Eguiluz, V. M., Chialvo, D. R., Cecchi, G. A., Baliki, M. & Apkarian, A. V. Scale-free brain functional networks. Phys. Rev. Lett. 94, 018102 (2005).
van den Heuvel, M. P., Stam, C. J., Boersma, M. & Hullshof Pol, H. E. Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain. NeuroImage 43, 528–539 (2008).
Baliki, M. N., Geha, P. Y., Apkarian, A. V. & Chialvo, D. R. Beyond feeling: Chronic pain hurts the brain, disrupting the default-mode network dynamics. J. Neurosci. 28, 1398–1403 (2008).
Expert, P. et al. Self-similar correlation function in brain resting state fMRI. J. R. Soc. Interface (in the press); preprint at http://arxiv.org/abs/1003.3682v1 [q-biol.NC] (2010).
Salvador, R. et al. Neurophysiological architecture of functional magnetic resonance images of human brain. Cerebral Cortex 15, 1332–1342 (2005).
Damoiseaux, J. S. et al. Consistent resting-state networks across healthy subjects. Proc. Natl Acad. Sci. USA 103, 13848–13853 (2006).
Broyd, S. J. et al. Default-mode brain dysfunction in mental disorders: A systematic review. Neurosci. Biobehav. Rev. 33, 279–296 (2009).
Zhang, D. & Raichle, M. E. Disease and the brains dark energy. Nature Rev. Neurol. 6, 15–28 (2010).
He, Y., Chen, Z. & Evans, A. Structural insights into aberrant topological patterns of large-scale cortical networks in Alzheimers disease. J. Neurosci. 28, 4756–4766 (2008).
Garrity, A. G. et al. Aberrant ‘default mode’ functional connectivity in schizophrenia. Am. J. Psychiatry 164, 450–457 (2007).
Laufs, H. et al. Temporal lobe interictal epileptic discharges affect cerebral activity in default mode brain regions. Hum. Brain Mapp. 28, 1023–1032 (2007).
Osorio, I. et al. Epileptic seizures: Quakes of the brain? Phys. Rev. E 82, 021919 (2010).
Chialvo, D. R. in Cooperative Behavior in Neural Systems: Ninth Granada Lectures (eds Marro, J., Garrido, P. L. & Torres, J. J.) 1–12 (AIP Conference Proceedings, 2007).
Bienenstock, E. & Lehmann, D. Regulated criticality in the brain? Adv. Complex Syst. 1, 361–384 (1998).
Magnasco, M. O., Piro, O. & Cecchi, G. A. Self-tuned critical anti-Hebbian networks. Phys. Rev. Lett. 102, 258102 (2009).
Levina, A., Herrmann, J. M. & Geisel, T. Dynamical synapses causing self-organized criticality in neural networks. Nature Phys. 3, 857–860 (2007).
Kinouchi, O. & Copelli, M. Optimal dynamical range of excitable networks at criticality. Nature Phys. 2, 348–352 (2006).
de Arcangelis, L. & Herrmann, J. Learning as a phenomenon occurring in a critical state. Proc. Natl Acad. Sci. USA 107, 3977–3981 (2010).
de Franciscis, S., Torres, J. J. & Marro, J. Unstable dynamics, nonequilibrium phases and criticality in networked excitable media. Phys. Rev. E (in the press); preprint at http://arxiv.org/abs/1007.4675v2 [cond-mat.dis-nn] (2010).
Honey, C. J., Kotter, R., Breakspear, M. & Sporns, O. Network structure of cerebral cortex shapes functional connectivity on multiple timescales. Proc. Natl Acad. Sci. USA 104, 10240–10245 (2007).
D.R.C. is with the National Research and Technology Council (CONICET) of Argentina. This work was supported by CONICET and by NIH NINDS NS58661. Thanks to E. Tagliazucchi and F. Lebensohn-Chialvo for reading the manuscript.
The author declares no competing financial interests.
About this article
Cite this article
Chialvo, D. Emergent complex neural dynamics. Nature Phys 6, 744–750 (2010). https://doi.org/10.1038/nphys1803
This article is cited by
Scientific Reports (2023)
Nature Physics (2023)
Nature Communications (2023)
Frontiers of Physics (2023)
Synchronization and oscillation behaviors of excitatory and inhibitory populations with spike-timing-dependent plasticity
Cognitive Neurodynamics (2023)