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## Lyapunov exponent estimation from a time series. Documentation added.

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A Matlab version of the Lyapunov exponent estimation algorithm of Wolf et al. -- Physica 16D, 1985.

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In Physica 16D (1985) we presented an algorithm that estimates the dominant Lyapunov exponent of a 1-D time series by monitoring orbital divergence. The algorithm was distributed for many years by the authors in Fortran and C. It has just been converted to Matlab. Documentation will be posted shortly.

mh oly

Ovee Matlab

### Ovee Matlab (view profile)

Elijah Tapiwa Chipato

jose monroy

Alan Wolf

### Alan Wolf (view profile)

If you have questions about the algorithm, PLEASE DON'T POST THEM HERE. Simply email me. This space is for comments and ratings, not conversations.

tnx a lot Sir Alan ... I found that . just one question . i have my own time series in order to calculate biggest LE ( just this and nothing more . just the final result number of time series ) . should i just replace my normalize time series and with your data ?

Alan Wolf

### Alan Wolf (view profile)

I've been asked more than once... where is the output (exponent estimate). This is discussed in the documentation (Lyapunews.pdf) - please read it. An output file is created when the program is run. The running estimate of the dominant exponent is the 4th column of numbers in that file. Discussed on page 16 of Lyapunews.

Hi Sir Alan . Tnx a lot for your work . i have a question sir .
where can i exactly find the largest lyapunove in output ? ( in documation mentioned approximately 2.1 )

Alan Wolf

### Alan Wolf (view profile)

You can’t get negative exponents because:

1) In a system with positive, negative, perhaps zero exponents, the average rate of orbital divergence is dominated by the term that grows fastest, which by definition, is the exponential term with an exponent that is the largest POSITIVE Lyapunov exponent. Negative exponents contribute, but a contribution like e^(-3t) won't be seen if there is also a term like e^(+2t).
2) In a system like the Lorenz attractor, negative exponents relate to transient decay towards the chaotic attractor. Your data set consists solely of post-transient data. Once you discarded the transients, there is not way to get them back.

Jiang Benny

### Jiang Benny (view profile)

Why cannot I get a negative Lyapunov exponent from this program?

Max Murphy

cbzeng

WENZHE HU

liu peng

Mei

### Mei (view profile)

Thanks very much Dr. Wolf.

Alan Wolf

### Alan Wolf (view profile)

There is no fundamental limit to the size/length of the time series. Modify the code (in C, Fortran, etc.) as regards memory requirements to suit your needs. Matlab may not be the best way to go for efficiency...

Mei

### Mei (view profile)

I have a question :whether the data points in the time series must be less than 32000 when I use this code，if it is more than 32000,what should I do?
Thank a lot Dr. Wolf !

Krishna Kumar

### Krishna Kumar (view profile)

Thanks a ton Dr. Wolf!

Arlene

### Arlene (view profile)

Thanks a bunch Alan!

jingbinchang

### jingbinchang (view profile)

Thaks very much dear Wolf.

Abhilash

Tak120

### Tak120 (view profile)

Thaks very much dear Wolf.

Alan Wolf

### Alan Wolf (view profile)

To Tak120 -- the program produces an output file. That file shows the convergence (hopefully!) of the exponent as orbital divergence is tracked through more and more of the input data file/time series.

Tak120

### Tak120 (view profile)

Thanks dear Wolf for this excellent code,
but i have a question : how can i find the result of Lyapunov Exponent from your code?
Thank you again !

mathew james

Phymath

Phymath

Ammar Dukhan

Ammar Dukhan

### Ammar Dukhan (view profile)

Thanks Dr. Alan .... the program is amazing.... I just have a simple notice, so a sub-file, Data.lor, should be Data2.lor inside a main program, testbench.m, in order to run..... again thank you....

Best Regards,
Ammar M Dukhan
PhD student at QUT

Vivek

### Vivek (view profile)

Please improve the documentation for this program. It is not very clear what the input/output arguments are.
Thanks!

Alan Wolf

### Alan Wolf (view profile)

There is nothing wrong with the code that I am aware of. If questions, feel free to email me at wolf@cooper.edu

Alan Wolf

Tak120

### Tak120 (view profile)

Dear Predrag,
Could you please give us the correct code.
Thank you

Predrag

### Predrag (view profile)

It has just been converted to Matlab with several syntax errors in code.