| Self- organized critical (SOC) systems are slowly driven interaction dominated threshold systems which may express cascades of events, called avalanches (Bak et al., 1987, Jensen, 1998). SOC was proposed to govern brain dynamics, because of its activity fluctuations over many orders of magnitude, its sensitivity to small input, and its long term stability (Bak, 1996; Jensen, 1998). The hallmark feature of SOC systems, a power law distribution f(s) for the avalanche size s, was found for neuronal avalanches recorded in vitro (Beggs and Plenz, 2003). In vivo electrophysiological recordings show avalanches, which are also compatible with SOC models (Priesemann et al., 2009). However, the neuronal avalanches recorded in vitro and in vivo can only be defined on a time scale of a few milliseconds and only when a rather small number of sampling sites are taken into account. If the activity of all neurons in the brain was sampled, one would not expect distinct neuronal avalanches separated by phases of silence, but rather continuous activity. This is in contrast to the requirements for SOC systems, which assume infinitesimally small drive. Here, we demonstrated that adding non- zero drive to self- organized critical models destroys the critical state, and continuous activity arises instead of distinct avalanches. Nevertheless, the long- term stability, the sensitivity to small input, and the activity fluctuations over many orders of magnitude can be preserved. The driven threshold systems can explain the electrophysiological activity recorded in the behaving monkey and in slices not only on the time scale of a few milliseconds but also on longer time scales. Although these driven threshold systems are only simple cellular automatons with locally interacting threshold elements, they express compact propagating waves, and their responses to input show the variability and reliability often observed in neuronal activity like evoked potentials. |
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