Lyapunov Exponent using OpenTSTool - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T08:35:44Z http://mathoverflow.net/feeds/question/75052 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75052/lyapunov-exponent-using-opentstool Lyapunov Exponent using OpenTSTool vinayashrestha 2011-09-09T23:28:54Z 2012-11-30T05:48:59Z <p>Has anyone calculated Lyapunov Exponents (LE) using OpenTSTool? It says it calculates the Largest Lyapunov exponent by <strong>computing the average exponential growth of the distance of neighboring orbits via the prediction error</strong>. So, I am trying to plot Lyapunov exponents for Chua's oscillator that is showing chaotic behavior.</p> <p>Hence, I am expecting a positive LE, a negative LE and a zero LE. But the plot I get is all positive values, and the values are pretty high as well, spanning fro 0 to 10. Can anyone tell me how to interpret this Lyapunov exponent plot?</p> <p>Thanks. </p> http://mathoverflow.net/questions/75052/lyapunov-exponent-using-opentstool/114929#114929 Answer by Harun Šiljak for Lyapunov Exponent using OpenTSTool Harun Šiljak 2012-11-29T20:54:41Z 2012-11-30T05:48:59Z <p>After a year, I am reviving this question to finally answer it. I hope it's not a bad thing. Reference you need is</p> <p><a href="http://www.physik3.gwdg.de/~ulli/pdf/P98b.pdf" rel="nofollow">U. Parlitz, Nonlinear Time-Series Analysis, in: Nonlinear Modeling - Advanced Black-Box Techniques, Eds. J.A.K. Suykens and J. Vandewalle, Kluwer Academic Publishers, Boston, 209-239, 1998.</a></p> <p>This chapter is the basis of OpenTSTool, and it contains almost all theoretical references. There you can learn that this tool uses Sato algorithm and see how the prediction error graph (the one you get) is converted to Lyapunov exponents (pages 223 and 224).</p>