While propagation of synchrony is usually short-lived in linearly coupled networks (a), it is persistent for a wide range of coupling parameters if the neurons are nonlinearly coupled (b,c).
The parameter scans illustrate this by varying the mean total input strengths of the excitatory and the inhibitory input in a network of neurons with connectivity. For each combination, synchronous activity was initiated with 100 neurons (a,b) or 75 neurons (c) and the stability of the temporal evolution was assessed. Blue coloring indicates stable propagation of synchrony, red and yellow coloring refers to unstable background activity before and after onset of propagation, and green coloring indicates unstable propagation (see Methods for details). White squres in (a) and (b) indicate the coupling strengths employed in Fig. 2a) and b), respectively. The large blue areas in the scans for nonlinearly coupled networks indicate that propagation of synchrony is stable in a wide range of parameters for such networks. This area is absent for linearly coupled networks as shown in (a), for smaller initial pulse sizes (e.g. 75 neurons) the number of successful trials is even smaller. In nonlinearly coupled networks with larger coupling strengths, an initial pulse size of 100 neurons can be larger than the upper bound of the propagation zone so that the chain is unstable (b) while for the same coupling parameters an initial pulse of size 75 neurons starts a stable chain (c). For smaller coupling strengths, an initial pulse size of 75 neurons can be insufficient to initiate stable propagation in contrast to a pulse of size 100 neurons.