The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 157–164 | Cite as

Evidence of low-dimensional chaos in magnetized plasma turbulence

  • T. ŽivkovićEmail author
  • K. Rypdal


We analyze probe data obtained from a toroidal magnetized plasma configuration suitable for studies of low-frequency gradient-driven instabilities. These instabilities give rise to field-aligned convection rolls analogous to Rayleigh-Benard cells in neutral fluids, and may theoretically develop similar routes to chaos. When using mean-field dimension analysis, we observe low dimensionality, but this could originate from either low-dimensional chaos, periodicity or quasi-periodicity. Therefore, we apply recurrence plot analysis as well as estimation of the largest Lyapunov exponent. These analyses provide evidence of low-dimensional chaos, in agreement with theoretical predictions. Our results can be applied to other magnetized plasma configurations, where gradient-driven instabilities dominate the dynamics of the system.


Lyapunov Exponent European Physical Journal Special Topic Normalize Mean Square Error Large Lyapunov Exponent Recurrence Plot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. K. Rypdal, S. Ratynskaia, Phys. Rev. Lett. 94, 225002 (2005) Google Scholar
  2. K. Rypdal, O. Garcia, Phys. Plasm. 14, 022101 (2007) Google Scholar
  3. A.Y. Ukhorskiy, M.I. Sitnov, A.S. Sharma, K. Papadopoulos, Ann. Geophys. 21, 1913 (2003) Google Scholar
  4. F. Takens, Dynamical Systems and Turbulence, edited by D. Rand, L.S. Young (Springer, Berlin, 1981), p. 366 Google Scholar
  5. H. Abarbanel, Analysis of Observed Chaotic Data (Springer, New York, 1996), p. 28 Google Scholar
  6. L. Cao, A. Mees, K. Judd, Physica D 121, 75 (1998) Google Scholar
  7. J.P. Eckmann, S.O. Kamphorst, D. Ruelle, Europhys. Lett. 5, 973 (1987) Google Scholar
  8. N. Marwan, J. Kurths, Phys. Lett. A 302, 299 (2002) Google Scholar
  9. M.C. Romano, M. Thiel, J. Kurths, W. von Bloh, Phys. Lett. A 330, 214 (2004) Google Scholar
  10. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007) Google Scholar

Copyright information

© EDP Sciences and Springer 2008

Authors and Affiliations

  1. 1.Department of Physics and TechnologyUniversity of TromsøTromsøNorway

Personalised recommendations