  The coupled discrete linear and Kerr nonlinear Schrodinger equations with
gain and loss describing transport on dimers with parity-time PT symmetric
potentials are considered. The model is relevant among others to experiments in
optical couplers and proposals on Bose-Einstein condensates in PT symmetric
double-well potentials. It is known that the models are integrable. Here, the
integrability is exploited further to construct the phase-portraits of the
system. A pendulum equation with a linear potential and a constant force for
the phase-difference between the fields is obtained, which explains the
presence of unbounded solutions above a critical threshold parameter. The
behaviour of all solutions of the system, including changes in the topological
structure of the phase-plane, is then discussed.
