Chaos and randomness: noise-induced phenomena in one-dimensional maps

Problems of complex behavior of random dynamical systems is investigated based on numerically observed noise-induced phenomena in Belousov-Zhabotinsky map (BZ map) and modified Lasota-Mackey map with presence of noise. We found that (i) both noise-induced chaos and noise-induced order robustly coexist, and that (ii) asymptotic periodicity of density is varied by noise amplitude. Applications to time series analysis are also discussed.