Sensitive boundary condition dependence of noise-sustained structure.

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 decrease (relaxation) of the comoving Lyapunov exponent (characterizing the convective instability) from upstream to downstream [K. Fujimoto and K. Kaneko, Physica D 129, 203 (1999)]. It is shown that a fractal BCD appears if the dynamics that represent the spatial change of the fixed point includes transient chaotic dynamics, and if appropriate intensity of noise is presented. By considering as an example a one-way-coupled map lattice, this theory for BCD is demonstrated.