Preprint: Linear stability analysis for networks of spiking neurons

[Masahiko Yoshioka]

Dear Connectionists,

I would like to announce the availability of the preprint of
my recent paper,

"Linear stability analysis of retrieval state in associative
memory neural networks of spiking neurons"

M. Yoshioka, Phys. Rev. E in press

Available at

   http://arxiv.org/abs/cond-mat/0209686

Abstract:

We study associative memory neural networks of the Hodgkin-Huxley
type of spiking neurons in which multiple periodic spatio-temporal
patterns of spike timing are memorized as limit-cycle-type attractors.
In encoding the spatio-temporal patterns, we assume the spike-timing-dependent
synaptic plasticity with the asymmetric time window. Analysis
for periodic solution of retrieval state reveals that if the
area of the negative part of the time window is equivalent to
the positive part, then crosstalk among encoded patterns vanishes.
Phase transition due to the loss of the stability of periodic
solution is observed when we assume fast alpha-function for direct
interaction among neurons. In order to evaluate the critical
point of this phase transition, we employ Floquet theory in which
the stability problem of the infinite number of spiking neurons
interacting with alpha-function is reduced into the eigenvalue
problem with the finite size of matrix. Numerical integration
of the single-body dynamics yields the explicit value of the matrix,
which enables us to determine the critical point of the phase
transition with a high degree of precision.

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Masahiko Yoshioka
Brain Science Institute, RIKEN
Hirosawa 2-1, Wako-shi, Saitama, 351-0198, Japan