Self-organized criticality in neural network models

Information processing by a network of dynamical elements is a delicate matter: Avalanches of activity can die out if the network is not connected enough or if the elements are not sensitive enough; on the other hand, activity avalanches can grow and spread over the entire network and override information processing as observed in epilepsy. Therefore, it has long been argued that neural networks have to establish and maintain a certain intermediate level of activity in order to keep away from the regimes of chaos and silence (Langton, 1990; Herz and Hopfield, 1995; Bak and Chialvo, 2001; Bornholdt and Röhl, 2003). Similar ideas were also formulated in the context of genetic networks where Kauffman postulated that information processing in these evolved biochemical networks would be optimal near the “edge of chaos”, or criticality, of the dynamical percolation transition of such networks (Kauffman, 1993). In the wake of self-organized criticality (SOC), it was asked if also neural systems were self-organized to some form of criticality (Bak et al., 1988). In addition, actual observations of neural oscillations within the human brain were related to a possible SOC phenomenon (Linkenkaer-Hansen et al., 2001). An early example of a SOC model that had been adapted to be applicable to neural networks is the model by Eurich et al. (2002). They show that their model of the random neighbor Olami-Feder-Christensen universality class exhibits (subject to one critical coupling parameter) distributions of avalanche sizes and durations which they postulate could also occur in neural systems. Another early example of a model for self-organized critical neural networks (Bornholdt and Röhl, 2001, 2003) drew on an alternative approach to self-organized criticality based in dynamical networks (Bornholdt and Rohlf, 2000). Here networks are able to self-regulate towards and maintain a critical system state, via simple local rewiring rules which are plausible in the biological context.