Sensitive boundary condition dependence of noise-sustained structure

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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.