From Self-Organized to Extended Criticality
UNIVERSITY OF NORTH TEXAS DENTON
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We address the issue of criticality that is attracting the attention of an increasing number of neurophysiologists. Our main purpose is to establish the specific nature of some dynamical processes that although physically different, are usually termed as critical, and we focus on those characterized by the cooperative interaction of many units. We notice that the term criticality has been adopted to denote both noise-induced phase transitions and Self-Organized Criticality SOC with no clear connection with the traditional phase transitions, namely the transformation of a thermodynamic system from one state of matter to another. We notice the recent attractive proposal of extended criticality advocated by Bailly and Longo, which is realized through a wide set of critical points rather than emerging as a singularity from a unique value of the control parameter. We study a set of cooperatively firing neurons and we show that for an extended set of interaction couplings the system exhibits a form of temporal complexity similar to that emerging at criticality from ordinary phase transitions. This extended criticality regime is characterized by three main properties i In the ideal limiting case of infinitely large time period, temporal complexity corresponds to Mittag-Leffler complexity ii For large values of the interaction coupling the periodic nature of the process becomes predominant while maintaining to some extent, in the intermediate time asymptotic region, the signature of complexity iii Focusing our attention on firing neuron avalanches, we find two of the popular SOC properties, namely the power indexes 2 and 1.5 respectively for time length and for the intensity of the avalanches.
- Anatomy and Physiology