Noisy map based on the PRC exhibits bistability and shows when one bistable mode is favored over the other.

<p>Experimental histograms corresponding to the data illustrated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002306#pcbi-1002306-g009" target="_blank">Fig. 9 B1, B2 and B3</a> with normalized delays of 0.09, 0.19 and 0.31 are shown for near antiphase (A1), bistability (B1) and near synchrony (C1) respectively. The output of the noisy map is shown for antiphase (A2), bistability (B2) and near synchrony (C2) for a hypothetical circuit constructed of two neurons with Type II inhibitory PRCs (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002306#pcbi-1002306-g002" target="_blank">Fig. 2B2</a>), at the same delays as for the corresponding experimental data. We introduced 4% heterogeneity in the intrinsic periods in order to reproduce the asymmetry in the experimental data. D) The right side shows the predicted solution structure for the hybrid circuit composed of two identical neurons with Type II inhibitory PRCs (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002306#pcbi-1002306-g002" target="_blank">Fig. 2B2</a>). The deterministic stable solutions are indicated by the black circles, and the unstable ones are indicated by red diamonds. The gray circles are the output of the noisy map based on the PRC. The histograms at left were constructed using the noisy map for delays corresponding to each labeled arrow on the solution structure at right, with A for near antiphase, B for bistability, and C for near synchrony. The axes of the histogram are aligned so the ordinate scale matches the time lag scale on the ordinate of the bifurcation structure. Each peak in the histograms is centered on a stable solution branch at the corresponding slice in the bifurcation diagram. For the symmetric case of two identical neurons, bistability (B) has five peaks and near synchrony (C) has three. The experimental histograms shown at the top and those produced by the noisy map and shown in the middle row have one less peak for bistability and near synchrony. This is because heterogeneity causes one neuron to lead consistently in the near synchronous mode instead of the random leader switching observed in the homogeneous circuit.