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Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons
Figure 4
Relationship between the PRC and the interaction function.
A: PRC of an aEIF neuron (top) spiking at 
and interaction functions 
(bottom) obtained for synaptic conductances with three different sets of synaptic time constants: 
, 
(blue), 
, 
(green); 
, 
(magenta), and 
. The synaptic current 
associated with each pair of time constants (center) illustrates the three synaptic timescales relative to the period 
. Note that 
shown here is received by the neuron at the beginning of its ISI. B: PRC (solid black) of an aEIF neuron spiking at 
and excitatory synaptic currents 
with 
, 
(dashed blue) received at three different phases. Assuming the input comes from a second, synchronous neuron, these phases represent three different conduction delays 
, 
, and 
. Note that synaptic input received at an earlier phase causes a larger peak of 
, due to the smaller value 
of the membrane potential which leads to a larger difference 
to the synapse's reversal potential 
. C: Interaction functions 
for pairs of neurons with the PRC shown in B, coupled by excitatory synapses with 
, 
, and delays 
and 
. The values of 
at 
are highlighted by blue circles. The slopes of 
, in terms of both left and right sided limits 
and 
, indicate whether the synchronous states are stable or unstable (see main text).
doi: https://doi.org/10.1371/journal.pcbi.1002478.g004