  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.

Chaotic Dynamics;Pattern Formation and Solitons