佐藤 譲（北海道大学 電子科学研究所 / 理学院数学専攻）
Noise-induced phenomena in one-dimensional maps
Interactions between deterministic chaos and stochastic randomness have been an important problem in nonlinear dynamical systems studies. Noise-induced phenomena are understood as a drastic change of natural invariant densities by adding external noise to a deterministic dynamics, resulting qualitative transition of observed nonlinear phenomena. Stochastic resonance, noise-induced synchronization, and noise-induced chaos are typical examples. The simplest mathematical model is given as one-dimensional maps perturbed by stochastic noise. In this presentation, we discuss typical behavior of noised dynamical systems based on numerically observed noise-induced phenomena in one-dimensional maps. Our observation indicates that (i) both noise-induced chaos and noise-induced order may coexist, and that (ii) asymptotical periodicity of densities bifurcates according to noise amplitude. A brief overview of nonlinear phenomena in random dynamical systems are also discussed with exemplifying an application for extracting random dynamics from a time-series.