Abstract
The supercritical short-wave oscillatory bifurcation is studied in finite systems using the amplitude (Ginzburg-Landau) equation. Numerical simulations show that a zero-flux boundary stabilizes sources of target patterns. As a result, stable sources attached to the boundary can exist at small overcriticality, under the condition of convective instability of the homogeneous steady state. Oscillating target patterns and alternating wave packets are formed if the coupling between left and right propagating waves is strong.