Connectionists: Synchronization in gap-junction-coupled neurons

[Masahiko Yoshioka]

Dear all,

We would like to announce another new paper on theoretical study of
spike synchronization in neural networks. In this paper we employ the
chaos synchronization theory to analyze stability of synchronization
in gap-junction-coupled neurons. We hope that the present study on gap
junctions and our previous study on chemical synapses
(http://arxiv.org/abs/nlin.PS/0504057) contribute together to a deeper
understanding of various synchronization phenomena in a large
population of neurons.


"Chaos synchronization in gap-junction-coupled neurons"

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

http://arxiv.org/abs/nlin.CD/0505054

Depending on temperature the modified Hodgkin-Huxley (MHH) equations
exhibit a variety of dynamical behavior including intrinsic chaotic
firing. We analyze synchronization in a large ensemble of MHH neurons
that are interconnected with gap junctions. By evaluating tangential
Lyapunov exponents we clarify whether synchronous state of neurons is
chaotic or periodic. Then, we evaluate transversal Lyapunov exponents
to elucidate if this synchronous state is stable against infinitesimal
perturbations. Our analysis elucidates that with weak gap junctions,
stability of synchronization of MHH neurons shows rather complicated
change with temperature. We, however, find that with strong gap
junctions, synchronous state is stable over the wide range of
temperature irrespective of whether synchronous state is chaotic or
periodic. It turns out that strong gap junctions realize the robust
synchronization mechanism, which well explains synchronization in
interneurons in the real nervous system.


Best regards,

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