  A set of coupled complex Ginzburg-landau type amplitude equations which
operates near a Hopf-Turing instability boundary is analytically investigated
to show localized oscillatory patterns. The spatial structure of those patterns
are the same as quantum mechanical harmonic oscillator stationary states and
can have even or odd symmetry depending on the order of the state. It has been
seen that the underlying Turing state plays a major role in the selection of
the order of such solutions.
