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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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© Author(s) 2014. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
09 Dec 2014
Review status
This discussion paper has been under review for the journal Nonlinear Processes in Geophysics (NPG). The revised manuscript was not accepted.
Transient behavior in the Lorenz model
S. Kravtsov, N. Sugiyama, and A. A. Tsonis Department of Mathematical Sciences, Atmospheric Science Group, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201–0413, USA
Abstract. Dynamical systems like the one described by the three-variable Lorenz model may serve as metaphors for complexity in nature. When natural systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz model by studying its trajectories initialized far away from the asymptotic attractor. Perhaps somewhat surprisingly, these transient trajectories exhibit complex routes and, among other things, sensitivity to initial conditions akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium.

Citation: Kravtsov, S., Sugiyama, N., and Tsonis, A. A.: Transient behavior in the Lorenz model, Nonlin. Processes Geophys. Discuss., 1, 1905-1917, doi:10.5194/npgd-1-1905-2014, 2014.
S. Kravtsov et al.
S. Kravtsov et al.


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Short summary
We studied transient behavior in numerical simulations of the three-variable Lorenz model initialized far away from the region of its asymptotic attractor. These transients were shown to have a range of durations, with the longest transients corresponding to the trajectories having largest average Lyapunov exponents and complex routes emulating sensitivity to initial conditions, as well as exhibiting the “ghost” attractors akin to their asymptotic siblings.
We studied transient behavior in numerical simulations of the three-variable Lorenz model...