  The dilation method is an important and useful way in experimentally
simulating non-Hermitian, especially $\cal PT$-symmetric systems. However, the
time dependent dilation problem cannot be explicitly solved in general. In this
paper, we consider a special two dimensional time dependent $\cal PT$-symmetric
system, which is initially set in the unbroken $\cal PT$-symmetric phase and
later goes across the exceptional point and enters the broken $\cal
PT$-symmetric phase. For this system, the dilation Hamiltonian and the
evolution of $\cal PT$-symmetric system are analytically worked out.
