  Sensitive boundary condition dependence (BCD) is reported in a convectively
unstable system with noise, where the amplitude of generated oscillatory
dynamics in the downstream depends sensitively on the boundary value. This BCD
is explained in terms of the manner in which the co-moving Lyapunov exponent
(characterizing the convective instability) decreases from upstream to
downstream. It is shown that a fractal BCD appears if the dynamics that
represent the spatial change of the fixed point includes transient chaotic
dynamics. By considering as an example a one-way-coupled map lattice, this
theory for BCD is demonstrated.
