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I am trying to figure out the equation below so that I can re-create it and use it for probability of dynamic systems in MATLAB.

enter image description here

I am trying to figure out what the enter image description here symbol stands for and how to use it with MATLAB.

If anyone can give me walkthrough of this equation with some test data, that would be more than appreciated.

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Where, exactly, did you encounter this expression? –  J. M. May 9 '11 at 16:27
    
This expression is used for prediction in dynamical systems. This above expression was found on en.wikipedia.org/wiki/Lyapunov_exponent –  Kyle Uithoven May 9 '11 at 16:43
    
"the rate of separation of infinitesimally close trajectories" is the key phrase; in practical work, your trajectories ought to be separated by an amount that is some small multiple of machine epsilon... –  J. M. May 9 '11 at 16:47
    
@Kyle: δ refers to a difference. –  Fabian May 9 '11 at 16:48
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Most of the time, it is possible to linearize the system around $Z_0$ (sometimes even analytically). Then the Lyapunov exponent is the eigenvalue of the Jacobian at $Z_0$ with the maximal real part. –  Fabian May 9 '11 at 16:49

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