Transient behavior in the Lorenz model

نویسندگان

  • Sergey Kravtsov
  • Noriyuki Sugiyama
  • Anastasios A. Tsonis
چکیده

Reply to previous reviews (of the published NPGD paper): We once again thank both reviewers for their comments, which we tried our best to reflect in the revised manuscript (all changes with respect to the previous version are highlighted). Reviewer 2 remains to be concerned with the alleged lack of novelty in our approach and results. While we have indeed been unaware of the previous work on the geometry of the Lorenz manifold — and we are very grateful to the reviewer for pointing this work out — we still think, after studying these papers, that our study is original and useful. In particular, earlier studies by Krauskopf, Osinga et al. have addressed in detail the topology of the Lorenz manifold, but they didn’t really focus on the transient behavior itself except in the context of preturbulence, which is a very different situation from the one studied in the present paper. The transient divergence of initially close trajectories we found, and the “ghost attractor” behavior go beyond the asymptotic fate of different initial condition in the Lorenz system, even in the global context, as understood from the structure of the Lorenz manifold. The complexity of the Lorenz manifold does not automatically indicate the disparity of the transient trajectories, as the reviewer tends to imply in his/her original comments. We do think that the Lorenz manifold is an important part of the story about the extreme transients in the Lorenz model (and we are excited about it!) — but its detailed role in transient dynamics still needs to be established in further studies.

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تاریخ انتشار 2014