  We discover presence of a hitherto unexplored type of resonance in a
parametrically excited Van der Pol oscillator. The oscillator also possesses a
state of anti-resonance. In the weak non-linear limit, we explain how to
practically get a complete picture of different states of limiting oscillations
present in the oscillator when the non-linear term therein is excited by an
arbitrary $2\pi$ periodic function of time. We also illustrate how two such
oscillators can be coupled to behave like a two-state switch allowing an sharp
change of value of amplitude for stable oscillations from one constant to
another.
