Biomedical Engineering Reference
In-Depth Information
Figure 2
. Model of the network generating episodic activity. (
A
) Justification for a mean-field
formulation. Neurons are connected to each other through random excitatory connections.
Neurons i, ii, ... are active together but their spikes are not synchronized. Spike rate can thus be
averaged, giving a smooth curve, the activity (network output) that is injected back into the
network. (
B
) Schematic representation of the model network. Network output (
a
) is fed back to
the neuron population through recurrent excitatory synapses. The amount of feedback is pro-
portional to the connectivity (
n
) and can be reduced by fast (
d
) and/or slow (
s
) synaptic depres-
sion. Network output can also be modulated by slow variations of the average cellular
threshold (R). (
C
) Sigmoidal input-output function of the network. Note that
a
(0) > 0, implic-
itly assuming that a few cells in the network are always discharging at low rate, providing a
background "input" to the network. Modified from Tabak et al. (36).
(
)
U
a
aa ansda
+=
¸¸¸
,
[1]
d
()
U
d
ddda
+=
,
[2]
d
()
U
s
ss sa
+=
,
[3]
d
or
()
UR R R
d
+=
a
.
[3']
