  We study the frequency and phase synchronization in two coupled identical and
nonidentical neurons with channel noise. The occupation number method is used
to model the neurons in the context of stochastic Hodgkin-Huxley model in which
the strength of of channel noise is represented by ion channel cluster size of
the initiation region of neuron. It is shown that frequency synchronization
only was achieved at arbitrary value of couple strength as long as two neurons'
channel cluster sizes are the same. We also show that the relative phase of
neurons can display profuse dynamic behavior under the combined action of
coupling and channel noise. Both qualitative and quantitative descriptions are
applied to describe the transitions between those behaviors. Relevance of our
findings to controlling neural synchronization experimentally is discussed.
