Talk:Transient chaos

From Scholarpedia

Superpersistent chaotic transients in spatiotemporal systems

The results concerning Supertransient Chaotic Transients found by Crutchfield and Kaneko (1988) by studying the map (9) + (10) have been shown to be wrong in a successive study by Politi, Livi, Oppo, Kapral [Europhys. Lett. 22, 571 (1993)] in that paper the authors have shown with accurate numerical simulations that the transient increases as simple exponential with the system size and not super-exponentially as reported by Crutchfield and Kaneko (1988). Moreover, the mechanisms underlying such a behaviour was termed Stable Chaos, since exponential transients occurs in spatially extended systems even for non chaotic maps and are due to finite amplitude effects (see the recent review: T. Tel and Y-C Lai, Phys Rep 460, 245 (2007)). This field has led to a fruitful research direction, not mentioned at all by Dr. Ying-Cheng Lai, in the last 20 years, which has found applications in field as different as chaotic synchronization and dynamics of neural networks (for a recent review see A. Politi and A. Torcini (2009) arXiv:0902.2545). I think that this article should be amended for the above mentioned reasons.

Alessandro Torcini