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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.

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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?2011-05-09
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    This expression is used for prediction in dynamical systems. This above expression was found on http://en.wikipedia.org/wiki/Lyapunov_exponent2011-05-09
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    "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...2011-05-09
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    @Kyle: δ refers to a difference.2011-05-09
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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.2011-05-09
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    @Fabian: A difference of what? What exactly should Z be? It appears that you can plug in a t?2011-05-09
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    You didn't still tell us how your dynamical system is defined. Typically, one would think about an ordinary differential equation (with respect to $t$). $Z(t)$ then defines the "coordinates" of the system at time $t$ and $Z_0$ at time $t=0$.2011-05-09
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    I don't know definition of my dynamical system. I am programming this in MATLAB so that any timeseries that is sent can be calculated against.2011-05-09
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    For the Lyapunov exponent you need the **difference** between two time series which are (initially) sufficiently close together.2011-05-09

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