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a
b
Fig. 13.3. Synchronous (a) and irregular (b) dynamics of three neurons in a sparse random
network [149]. Both dynamics may coexist in the same network and external stimulations can
induce switching between them, cf. also Fig. 13.4. (Modied from [149].)
synchronizing
desynchronizing
perturbations
(i)
(ii)
(iii)
t
60
300
Fig. 13.4. Transitions between irregular and synchronous states due to external input signals.
Synchronized excitatory external input (i) causes the dynamics to assume the synchronous state.
The synchronous state is stable: A suciently small desynchronizing perturbation (ii) does not
lead to the irregular state. Only after strong desynchronizing signals (iii), e.g. induced by a large
number of random inhibitory and excitatory input spikes, the system switches back to the irregular
state. (Modied from [149].)
excitatorily coupled networks of leaky (and non-leaky [136]) IF-like neurons if the
interactions exhibit zero delay ([108], see also [52]), but it is unstable in the pres-
ence of arbitrarily small delays in globally and more complex connected excitatory
networks [40, 41, 148, 149]. If the coupling is inhibitory, however, synchrony might
occur and even be predominant [106, 149, 152, 161] in the presence of interaction
delays as well, cf. Figs. 13.3a, 13.4. Noise in such systems aects synchrony in a
non-trivial way [26].
In globally coupled or spatially extended homogeneous networks of spiking units
also less symmetric solutions exist, including waves [21], periodic localized activ-
ity [134] and cluster states [40] exist that are well known from smoothly coupled
systems.
