Criticality in a simple model for brain functioning

Statistical study of magnetic disturbances at the Earth's surface

“…Among the mechanisms that could lead to powerlaw distributions we can mention some that, for us, have a more mathematical than physical sense (because it is very difficult to imagine populations with different probability distribution functions in systems with a considerable degree of turbulence as the Sun surface and the magnetosphere must be), which are the combination of exponentials and the superposition of distributions. Another formalism that could also lead to power-laws (Gell-mann and Tsallis, 2004) remains with some obscure physical significance (the theory is based on a parameter usually represented by ''q'' that up to now does not have a clear physical meaning) among other problems (Papa, 1998). Wanliss (2005) found power-law distributions with a single exponent (that depends on time and also that varies from quiet to active intervals).…”

“…Modelling of this system posses huge challenges and will be addressed in future works. It has been shown (da Silva et al, 1998) that the introduction of a refractory time (time after the release of energy by an element of a threshold system during which the element is unable of further energy releases) in some threshold models leads to a variation in the exponents of power-laws. Although is not at all clear what could be physical basis of a refractory time for the present problem we believe that the first steps will be along these lines.…”

Metastability, criticality and phase transitions in brain and its models

“…Bornhold & Rohlf (2003) extend critical self-organization to the evolution of network topology. Critical network models were also studied by Wakeling (2003) and da Silva (1998). Referring to the previously cited studies of Beggs & Plens (2003), Haldeman and Beggs (2005) contribute the additional important observation that branching network models with recurrent connectivity can account for power law relations at critical points, and display metastable states at branching parameters, intermediate between sub-and supercritical values.…”

Mo6S3I6 molecular wires: From a one‐dimensional quantum fluid to self‐organized critical self‐assembled networks

“…4 indicates that the network is scale‐invariant over a large range. Such self‐organized critical behaviour occurs in neural network systems 8 and leads to the functionality of the brain for example 9. Neuron functionality operates on the basis of the propagation of electrical signals (action potentials) through the network, where the vertices (the synapses) act as nonlinear elements that process the signals, while the axons transmit the signals.…”