Noise-induced chaos

Noise-induced chaos is an interesting phenomenon. However, it is a subtle issue because of the difficulty in distinguishing between true low-dimensional chaos and noise. In this review article, we consider how to define noise-induced chaos and what constitutes a test for noise-induced chaos. The mechanism for noise-induced chaos is studied by considering the long-term growth rate of the logarithmic displacement curves. In particular, we have identified three types of diffusional processes, with the third type, the anomalous diffusion, being the precursor of noise-induced chaos. A number of dynamical systems showing different types of diffusional processes are discussed. We have also pointed out when and how a nonlinear noisy system may be mistaken as a chaotic system in general and noise-induced chaos in particular.