Fortran 90 Routine: LAMBDA_LOG_DISP
By: Jianbo Gao and Johnny Lin
If you send me [Johnny] <[email protected]> your email address, I'll let you know of any major bugs that are found in this library.
Note last updated: 26 Jun 2002
In this note we describe criteria for choosing a number of the parameters for the routine:
The choice of the number of points (local variable nn) to use in the calculations is one informed by experience, a balance of accuracy and computational expense. If you are studying chaotic behavior, if the dimension is not too high, then a few thousand points of nn gives similar results as that with much larger nn. For diffusional scaling laws, depending on how long the scaling is, nn is preferred to be larger, if possible. But it is limited by nxp (nxp is the length of the input timeseries):
As Gao and Zheng (1994) points out, it is best to remove tangential motion effects before calculating lambda. In that study, |i-j| < w (where w = (m-1)L, the embedding window) were removed. However, one can use |i-j| < 10 as a removal criteria, which is the default setting for the routine. If one can choose w, it's better for it to be very large so that the effect of any kind of correlation (more precisely, orbital or tangential motions) can be fully eliminated.
Gao, J. and Z. Zheng (1994): Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time series, Phys. Rev. E, Vol. 49, No. 5, pp. 3807-3814.