Mean-Field Theory of Irregularly Spiking Neuronal Populations and Working Memory in Recurrent Cortical Networks - Computational Neuroscience: A Comprehensive Approach - page 476

might come about with a positive real eigenvalue: this is a mean rate instability,
which typically occur in a network with strong recurrent excitation. Alternatively, an
instability associated with a positive real part of a complex eigenvalue signals a Hopf
bifurcation. If the bifurcation is supercritical, the network exhibits a synchronized
oscillation with a frequency close to Im

( )

. For more details on this approach, see
[1] for the scenario with a simplified model with purely external noise, and [24] for
a model with recurrent noise.

l

References
[1] L. F. Abbott and C. van Vreeswijk (1993), Asynchronous states in a network
of pulse-coupled oscillators, Phys. Rev. E, 48 : 1483-1490.
[2] M. Abramowitz and I. A. Stegun (1970), Tables of Mathematical Functions,
Dover Publications, NY.
[3] E. D. Adrian (1928), The Basis of Sensation: The Action of the Sense Organs ,
W. W. N o r t o n : N Y.
[4] B. Ahmed and J. C. Anderson and R. J. Douglas and K. A. Martin and J. C. Nel-
son, Polyneuronal innervation of spiny stellate neurons in cat visual cortex,
J. Comp. Neurol., 341 : 39-49.
[5] S. Amari (1977), Dynamics of pattern formation in lateral-inhibition type neu-
ral fields, Biol. Cybern., 27 : 77-87.
[6] D. J. Amit (1995), The Hebbian paradigm reintegrated: local reverberations as
internal representations, Behav. Brain Sci., 18 : 617.
[7] D. J. Amit and M. V. Tsodyks (1992), Effective neurons and attractor neural
networks in cortical environment, Network , 3 , 121-137.
[8] D. J. Amit and M. V. Tsodyks (1991), Quantitative study of attractor neural
network retrieving at low spike rates I: Substrate - spikes, rates and neuronal
gain, Network , 2 : 259-274.
[9] D. J. Amit and M. V. Tsodyks (1991), Quantitative study of attractor neural net-
work retrieving at low spike rates II: Low-rate retrieval in symmetric networks,
Network , 2 : 275.
[10] D. J. Amit and N. Brunel (1997), Dynamics of a recurrent network of spiking
neurons before and following learning, Network, 8 : 373-404.
[11] D. J. Amit and N. Brunel (1997), Model of global spontaneous activity and
local structured activity during delay periods in the cerebral cortex, Cerebral
Cortex , 7 : 237-252.
[12] D. J. Amit and N. Brunel and M. V. Tsodyks (1994), Correlations of cortical