  We provide a systematic analysis of a prototypical nonlinear oscillator
system respecting PT-symmetry i.e., one of them has gain and the other an equal
and opposite amount of loss. Starting from the linear limit of the system, we
extend considerations to the nonlinear case for both soft and hard cubic
nonlinearities identifying symmetric and anti-symmetric breather solutions, as
well as symmetry breaking variants thereof. We propose a reduction of the
system to a Schr\"odinger type PT-symmetric dimer, whose detailed earlier
understanding can explain many of the phenomena observed herein, including the
PT phase transition. Nevertheless, there are also significant parametric as
well as phenomenological potential differences between the two models and we
discuss where these arise and where they are most pronounced. Finally, we also
provide examples of the evolution dynamics of the different states in their
regimes of instability.
