Īlthough the precise neuronal mechanisms leading to the observed scale-free avalanche behavior is still uncertain after almost 20 years since their discovery, the commonly agreed upon paradigm is that this collective neuronal avalanche activity represents a unique and specialized pattern of brain activity that exists somewhere between the oscillatory, wave-like coherent activity and the asynchronous and incoherent spiking. It was also hypothesized that an existence of crucial events facilitates information transmission in various states of brain functioning. Crucial events, as a manifestation of criticality, have been discussed in using Diffusion Entropy Analysis. This discovery has generated significant interest in the role and the importance of criticality in brain activity. Ĭoherent macroscopic behavior arising from seemingly incoherent microscopic processes naturally suggests the influence of critical phenomena, a potential model from brain activity that was bolstered by the experimental discovery of the “neuronal avalanches” where both spatial and temporal distributions of spontaneous propagating neuronal activity in 2D cortex slices were shown to follow scale-free power laws. Linking these two seemingly disparate classes to explain the emergence of oscillatory rhythms from incoherent activity is essential to understanding brain function and is typically posed in the form using the construct of networks of incoherently spiking neurons. The second class focusses on the asynchronous, seemingly incoherent spiking activity at scales of a single neuron and often uses various ad hoc neuron models to describe this activity. The first class includes a variety of the oscillatory and wave-like patterns that show relatively high level of coherence across a wide range of spatial and temporal scales. The standard view of brain electromagnetic activity classifies this activity into two significant but essentially independent classes. The complexity of oscillatory and wave patterns across a wide range of spatial and temporal scales of brain activity results in multiple independent models for these activity patterns. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order non-linear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. The theory of the weakly evanescent non-linear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different non-linear side of wave processes abundant in cortical tissue. 2Center for Functional MRI, University of California, San Diego, San Diego, CA, United StatesĪnalytical expressions for scaling of brain wave spectra derived from the general non-linear wave Hamiltonian form show excellent agreement with experimental “neuronal avalanche” data.1Center for Scientific Computation in Imaging, University of California, San Diego, San Diego, CA, United States.
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