Calculation of the Lyapunov exponents of a time series
The Lyapunov exponents are defined as follows :
For a discrete dynamical system
they are the logarithmic eigenvalues of the matrix
where J is the Jacobian matrix.
The exponents may be seen as the average exponential growth rates of
initially close points under the flow generated by f. By convention,
they are numbered from the largest to the smallest,
The set is the Lyapunov spectrum. It is calculated using the parameters
- embedding dimension m,
- number M of neighbours in phase space taken into account and
- degree pd of the fitting polynome.
The results of "Lyapunov spectrum" including the Lyapunov exponents, the sum of
the Lyapunov exponents, and the Kaplan-Yorke-Dimension appear in
the message window.
Warning: Phase space calculations on long signals are computationally very expensive, and can lead to large response times of the program. Try to use small radii and low embedding dimensions if possible.
Correlation dimension, Correlation integral,
Largest Lyapunov exponent (LLE), Momentary largest Lyapunov exponent,
Pointwise correlation dimension (PD2), Pointwise correlation integral.