  We investigate the phase structure of two-color QCD at both real and
imaginary chemical potentials mu, performing lattice simulations and analyzing
the data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model.
Lattice QCD simulations are done on an 8^3 times 4 lattice with the
clover-improved two-flavor Wilson fermion action and the renormalization-group
improved Iwasaki gauge action. We test the analytic continuation of physical
quantities from imaginary mu to real mu by comparing lattice QCD results
calculated at real mu with the result of analytic function the coefficients of
which are determined from lattice QCD results at imaginary mu. We also test the
validity of the PNJL model by comparing model results with lattice QCD ones.
The PNJL model is good in the deconfinement region, but less accurate in the
transition and confinement regions. This problem is improved by introducing the
baryon degree of freedom to the model. It is also found that the vector-type
four-quark interaction is necessary to explain lattice data on the quark number
density.
