We consider a modified version of the well-known 2d vdP oscillator with a new
non-Hermitian interaction. The usual perturbative approach fails to provide the
classical dynamics of the system as the classical solutions become divergent in
the long time limit. These kinds of divergences are similar to what occurs in
quantum field theory and critical phenomena. The Renormalization Group (RG)
technique for the dynamical system has been used to eliminate the divergences
in the perturbative solution of the 2d vdP oscillator and to provide a
physically acceptable solution which is shown to be consistent with numerical
study. We further investigate the model in the framework of non-Hermitian
quantum mechanics to show the PT phase transition in the system.Comment: 12 pages, Latex, 6 Fig