Connectionists: Synchronization in an ensemble of neurons

[Masahiko Yoshioka]

Dear all,

We would like to announce a new paper on the theoretical study of
spike synchronization in neural networks.  We developed the analytical
method to clarify stability of synchronization in a large ensemble
neurons for arbitrary neuron dynamics and arbitrary strength of
interactions.


"Cluster synchronization in an ensemble of neurons interacting
through chemical synapses"

M. Yoshioka, Phys. Rev. E, in press.

http://arxiv.org/abs/nlin.PS/0504057

In networks of periodically firing spiking neurons that are
interconnected with chemical synapses, we analyze cluster state, where
an ensemble of neurons are subdivided into a few clusters, in each of
which neurons exhibit perfect synchronization. To clarify stability of
cluster state, we decompose linear stability of the solution into two
types of stabilities: stability of mean state and stabilities of
clusters. Computing Floquet matrices for these stabilities, we clarify
the total stability of cluster state for any types of neurons and any
strength of interactions even if the size of networks is infinitely
large. First, we apply this stability analysis to investigating
synchronization in the large ensemble of integrate-and-fire (IF)
neurons. In one-cluster state we find the bifurcation due to the
change of stability of a cluster, which elucidates that in-phase
synchronization of IF neurons occurs with only inhibitory
synapses. Then, we investigate entrainment of two clusters of IF
neurons with different excitability. IF neurons with fast decaying
synapses show the low entrainment capability, which is explained by a
pitchfork bifurcation appearing in two-cluster state with change of
synapse decay time constant. Second, we analyze one-cluster state of
Hodgkin-Huxley (HH) neurons and discuss the difference in
synchronization properties between IF neurons and HH neurons.


Best regards,

Masahiko Yoshioka
The Brain Science Institute
The Institute of Physical and Chemical Research (RIKEN)