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Short Conduction Delays Cause Inhibition Rather than Excitation to Favor Synchrony in Hybrid Neuronal Networks of the Entorhinal Cortex

Figure 4

Graphical method for determining the periodic modes a two neuron circuit with conduction delays can exhibit.

A. Periodicity constraints imposed by a pattern in which a spike in one neuron influences via a feedback loop the timing of the very next spike (k = 1) in the same neuron. B. Periodicity constraints imposed by a pattern in which a spike in one neuron influences via a feedback loop the timing of the second spike, but not the very next spike (k = 2) in the same neuron. C. Curves constructed, one for each neuron, for two identical neurons with a PRC as in Fig. 2A1, using the dependence of the stimulus and recovery intervals on the phase. The abscissa and ordinate points are reversed for one neuron as compared to the other so that intersections of the curves satisfy the appropriate periodicity constraints given in A or B. C1. At a normalized delay of 0.04, the open circles indicate unstable modes with two unequal time lags; either neuron can lead so there are two bistable modes. The dark circle indicates that the antiphase mode with two equal time lags is unstable. For stable points, the black curve is steeper than the red at the point of intersection. C2. For a normalized time lag of 0.40, the antiphase mode becomes stable as indicated by the open circle. C3. For normalized delays of 0.80, synchrony with one zero time lag becomes stable. D. The graphical method was applied at each value of the normalized delay in increments of 0.02. The time lags were calculated using the algebraic relationship of these quantities with the stimulus and recovery intervals shown in A or B as appropriate. Only time lags associated with stable modes (X symbols) were plotted. In addition, the network period, or sum of the time lags, was plotted as the gray circles.

Figure 4

doi: https://doi.org/10.1371/journal.pcbi.1002306.g004