At the Edge of Chaos: Real-time Computations and Self-Organized Criticality in Recurrent Neural Networks

This network model is similar to the one we have considered in [4]. However it differs in two important aspects: a) By using states xi {0, 1} we emphasis the asymmet- ric information encoding by spikes prevalent in biological neural systems and b) it is more general in the sense that the Gaussian distribution from which the non-zero weights are drawn is allowed to have an arbitrary mean R. This implies that the network activity a N t 1 x N i 1 i,t can vary considerably for different parameters (compare Figure 1) and enters all the calculations discussed in the rest of the paper. The top row of Figure 1 shows typical examples of ordered, critical and chaotic dynamics (see the next section for a definition of order and chaos). The system parameters corresponding to each type of dynamics are indicated in the lower panel (phase plot). We refer to the (phase) transition from the ordered to the chaotic regime as the critical line (shown as the solid line in the phase plot). Note that increasing the variance 2 of the weights consistently leads to chaotic behavior.