  A particle system with a (2+1)D exotic Newton-Hooke symmetry is constructed
by the method of nonlinear realization. It has three essentially different
phases depending on the values of the two central charges. The subcritical and
supercritical phases (describing 2D isotropic ordinary and exotic oscillators)
are separated by the critical phase (one-mode oscillator), and are related by a
duality transformation. In the flat limit, the system transforms into a free
Galilean exotic particle on the noncommutative plane. The wave equations
carrying projective representations of the exotic Newton-Hooke symmetry are
constructed.
