Hi Mark,

I have done a calculation of Lypunov exponents a long time ago, for an equation describing directional solidification at high speeds. The reference  is: K. Kassner, C. Misbah, H. Müller-Krumbhaar, A. Valance, Directional solidification at high speed. II. Transition to chaos, Phys. Rev. E 49, 5495 (1994). Details of the numerical approach, which was adapted from Ref. 21, are given in Appendix B. In particular, we had a very inelegant but useful modification that allowed us to calculate just a few Lyapunov exponents (the positive ones plus one or two of the largest negative ones). If you need just the largest one, that can be done in a simple and elegant way (essentially, you do a straightforward time integration of the variational equation).

Hope this is useful.

Dear Prof. Bradley,

 I suggest you check out the links below :

http://www.chebfun.org/examples/pde/Kuramoto.html

http://www.chebfun.org/examples/ode-nonlin/LyapunovExponents.html

I hope this should help.

Best regards.

Dear Klaus,

Many thanks, your input is very helpful.  We would probably just compute the largest Lyapunov exponent, at least to start.  Could you provide a reference for the simple and elegant method you said could be used to do this?

Best regards,

Mark

Dear Mark,

The elegant method for one Lyapunov exponent is just the method described in the paper without repeated solution of the variational equation (our method for several exponents was inelegant because of the necessity of that repetition; for the largest exponent only, no repetitions are necessary). The method of the paper is essentially taken from Ref. 21, i.e. Chua's book.

Dear Prof. Bradley,

I suggest you check out the link below :

http://www.chebfun.org/examples/ode-nonlin/LyapunovExponents.html

Best regards,