A chaotic map with a flat segment can produce a noise-induced order

Matsumoto and Tsuda studied the effects of noise on chaos in a one-dimensional Belousov-Zhabotinsky (BZ) map and found noise-induced order, that is, an external noise destroys a chaotic behavior and produces some kind of order (periodicities). This phenomenon is very interesting in understanding the relation between chaos and natural phenomena. The present paper proposes a unimodal piecewise linear map which has a flat segment. It is shown numerically that the noise-induced order can be observed in this simple map in the same way as the BZ map. These numerical results clarify the mechanism of noise-induced order.