When Can Noise Induce Chaos?

Crutchfield et al. observed that noise truncates period-doubling cascade and induces chaos. To date, however, very little low-dimensional chaos has been unambiguously identified experimentally. This discrepancy stimulates us to reexamine the noisy logistic map. We find that noise can indeed induce chaos. However, this is not associated with the main $2^n$ cascade. We identify three basic conditions for noise to induce chaos. We also show that when noise induces chaos the complete period-doubling cascade is inhibited, otherwise the cascade is simply masked by noise.