Title
Shil'Nikov Chaos In The 4D Lorenz-Stenflo System Modeling The Time Evolution Of Nonlinear Acoustic-Gravity Waves In A Rotating Atmosphere
Keywords
Lorenz-Stenflo system; Shil'nikov analysis; Smale horseshoe chaos
Abstract
The Lorenz-Stenflo system serves as a model of the time evolution of nonlinear acoustic-gravity waves in a rotating atmosphere. In the present paper, we study the Shil'nikov chaos which arises in the 4D Lorenz-Stenflo system. The analytical and numerical results constitute an application of the Shil'nikov theorems to a 4D system (whereas most results present in the literature deal with applying the Shil'nikov theorems to 3D systems), which allows for the study of chaos along homoclinic and heteroclinic orbits arising as solutions to the Lorenz-Stenflo system. We verify the observed chaos via competitive modes analysis - a diagnostic for chaotic systems. We give an analytical test, completely in terms of the model parameters, for the Smale horseshoe chaos near homoclinic orbits of the origin, as well as for the case of specific heteroclinic orbits. Numerical results are shown for other cases in which the general analytical method becomes too complicated to apply. These results can be extended to more complicated higher-dimensional systems governing plasmas, and, in particular, may be used to shed light on period-doubling and Smale horseshoe chaos that arises in such models. © 2013 Springer Science+Business Media Dordrecht.
Publication Date
6-1-2013
Publication Title
Nonlinear Dynamics
Volume
72
Issue
4
Number of Pages
837-851
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1007/s11071-013-0756-4
Copyright Status
Unknown
Socpus ID
84878587719 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84878587719
STARS Citation
Van Gorder, Robert A., "Shil'Nikov Chaos In The 4D Lorenz-Stenflo System Modeling The Time Evolution Of Nonlinear Acoustic-Gravity Waves In A Rotating Atmosphere" (2013). Scopus Export 2010-2014. 7047.
https://stars.library.ucf.edu/scopus2010/7047