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Gottwald Melborune (0–1) Test for Chaos in a Plasma : Volume 19, Issue 1 (10/01/2012)

By Chowdhury, D. R.

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Book Id: WPLBN0003974117
Format Type: PDF Article :
File Size: Pages 4
Reproduction Date: 2015

Title: Gottwald Melborune (0–1) Test for Chaos in a Plasma : Volume 19, Issue 1 (10/01/2012)  
Author: Chowdhury, D. R.
Volume: Vol. 19, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2012
Publisher: Copernicus Gmbh, Göttingen, Germany

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Lahiri, S., Chowdhury, D. R., & S. Iyenga, A. N. (2012). Gottwald Melborune (0–1) Test for Chaos in a Plasma : Volume 19, Issue 1 (10/01/2012). Retrieved from http://www.ebooklibrary.org/


Description
Description: Techno India, EM4/1, Sector V, Kolkata-700091, India. Plasma is a highly complex system exhibiting a rich variety of nonlinear dynamical phenomena. In the last two decades or so there has been a spurt of growth in exploring unconventional nonlinear dynamical methods of analysis, like chaos theory, multi fractal analysis, self organized criticality etc. of experimental data from different plasma systems. Investigation of fluctuating plasma parameters is very important since they are correlated with transport of particles, and energy. In time series analysis, it is considered of key importance to determine whether the data measured from the system is regular, deterministically chaotic, or random. The two important parameters that are in general estimated are the correlation dimension and the Lyapunov exponent. Though correlation dimension helps in determining the complexity of a system, Lyapunov exponent reveals if the system is chaotic or not and also helps in prediction to some extent. In spite of its extensive usage, estimation of Lyapunov exponent can be quite tedious and sometimes suffers from some disadvantages like reliability in the presence of noise, requirement of phase space reconstruction etc., and hence it is necessary to explore other possibilities of estimating the chaoticity of a data. In this paper we have analysed for chaoticity, the nonlinear floating potential fluctuations from a glow discharge plasma system by the 0–1 test and compared it with the results obtained from Lyapunov exponent.

Summary
Gottwald Melborune (0–1) test for chaos in a plasma

Excerpt
Cheung, P. Y. and Wong, A. Y.: Chaotic behaviour and periodic doubling in plasmas, Phys. Rev. Lett., 59, 551–554, 1987.; Ding Weixing, Huang Wei, Wang Xiaodong, and C. X. Yu: Chaos in glow discharge plasma, Phys. Rev. Lett. 70, 170–173,1993.; Dinklage, A., Wilke, C., and Klinger, T.: Spatiotemporal response of stochastic resonance in an excitable discharge plasma, Phys. Plasmas, 6, 2968–2971, 1999.; Gottwald, G. A. and Melbourne, I.: A new test for chaos in a deterministic system, Proc. Roy. Soc. A, 460, 603–611, 2004.; Gottwald, G. A. and Melbourne, I.: Testing for chaos in a deterministic system with noise Physica D, 460, 212, 100–110, 2005.; Nurujjaman, M. D. and Sekar Iyengar, A. N.: Realization of SOC behaviour in a dc glow discharge plasma, Phys. Lett. A, 360, 717–721, 2007.; Klinger, T., Greiner, T., Rohde, A., Piel, A., and Koepke, M. E.: Van der Pol behaviour of relaxation oscillations in a periodically driven thermionic discharge, Phys. Rev. E, 52, 4316–4327, 1995.; Lin, I. and Jeng-Mei, L.: Experimental observation of stochastic resonance like behaviour of autonomous motion in weakly ionized rf magnetoplasmas, Phys. Rev. Lett., 74, 3161–3164, 1995.; Nurujjaman, M. D., Sekar Iyengar, A. N., and Parmananda, P.: Noise invoked resonances near homoclinic bifurcation in the glow discharge plasma, Phys. Rev. E, 78, 026406-1–026406-5, 2008.; Rosenstein, M. T., Collins, J. J., and De Luca, C. J.: A practical method for calculating largest Lyapunov exponent for small data sets, Physica D, 65, 117–134, 1993.

 

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