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Transient Behavior in the Lorenz Model : Volume 1, Issue 2 (09/12/2014)

By Kravtsov, S.

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Book Id: WPLBN0004020087
Format Type: PDF Article :
File Size: Pages 13
Reproduction Date: 2015

Title: Transient Behavior in the Lorenz Model : Volume 1, Issue 2 (09/12/2014)  
Author: Kravtsov, S.
Volume: Vol. 1, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2014
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Tsonis, A. A., Sugiyama, N., & Kravtsov, S. (2014). Transient Behavior in the Lorenz Model : Volume 1, Issue 2 (09/12/2014). Retrieved from http://www.ebooklibrary.org/


Description
Description: Department of Mathematical Sciences, Atmospheric Science Group, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201–0413, USA. 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.

Summary
Transient behavior in the Lorenz model

Excerpt
Cushing, J. M., Dennis, B., Desharnais, R. A., and Constantino, R. F.: Moving toward an unstable equilibrium: saddle nodes in population systems, J. Anim. Ecol., 67, 298–306, 1998.; Ghil, M. and Childress, S.: Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics, Springer-Verlag, New York, 1987.; Hastings, A.: Transients: the key to long-term ecological understanding?, Trends Ecol. Evol., 19, 39–46, 2004.; Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130–141, 1963.; Saltzman, B.: Finite amplitude free convection as an initial value problem – I, J. Atmos. Sci., 19, 329–341, 1962.; Shimizu, T. and Morioka, N.: Transient behaviour in periodic regions of the Lorenz model, Phys. Lett. A, 69, 148–150, 1978.; Sparrow, C.: The Lorenz Equations: Bifurcation, Chaos, and Strange Attractors,. Springer-Verlag, New York, 1982.; Tsonis, A. A.: Chaos: from Theory to Applications, Springer, New York, 274 pp., 1992.; Yorke, J. A. and Yorke, E. D.: The transition to sustained chaotic behaviour in the Lorenz model, J. Stat. Phys. 21, 263–277, 1979.

 

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