Answer gives a software for calculating conditional Lyapunov exponent (CLE) for coupled oscillators in chaos synchronization. However, it is hard to follow and there is no graphical output of the plot (and it is in C, more complex). Does anyone know how to modify the LET Toolbox which is very good for uncoupled system but I do not understand how to work with synchronized system so as to accommodate the CLE.

  1. I have a confusion regarding how to include the driver signal while calculating the Jacobian matrix for CLE since theory says that CLE is found for the response system,so don't we have to find the Jacobian for the driver as well as the response system for similar oscillators(drive and response). Or should we consider both the drive and response system in the software and proceed as if it is a single system?
  2. How to accommodate an external forcing like a random process in a state equation if any in CLE.
  3. Is there any other implementation for CLE?

thank you

  • $\begingroup$ Why is this tagged with "quantum mechanics"? $\endgroup$
    – AlexE
    Commented Nov 11, 2014 at 8:52

1 Answer 1


Here is a link to an old paper in J Comp Phys which computes the LE for coupled random dynamical systems http://mesoscopic.mines.edu/acoustics-old/preprints/lyapunov.pdf Perhaps you will find it more readable. It's a stable, well-tested algorithm. The code was developed by my co-author who is now at KU (in case you want the code).

  • $\begingroup$ Thanks for the link but it's not opening? @JohnS, also we can discuss Dynamical Systems and chaos in this chatroom!! $\endgroup$
    – BAYMAX
    Commented Jun 28, 2018 at 6:38
  • $\begingroup$ Here's a link that seems to work: citeseerx.ist.psu.edu/viewdoc/… $\endgroup$
    – JohnS
    Commented Jun 29, 2018 at 14:41

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