We have experimentally obtained time series. We are building a trajectory in the phase space: the value of a time series - the rate of change of values (first derivative). How to calculate the dimension of the resulting trajectory?
Try to use TISEAN (time series analysis) http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/index.html
Try to use TISEAN (time series analysis) http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/index.html
What type of dimension are you trying to compute - embedding dimension, fractal dimension? What software are you interested in using? Are there other dynamical parameters you would likely compute later?
These will guide me in recommending a code for you. In the interim, if you are using MATLAB, there are several routines you can use to compute the embedding dimension.
Hi Samuel. Thank you for your interest in the issue. The phase trajectory on the plane, ie, in the two-dimensional state space has a self-intersection. I need to compute what the dimension of the state space is sufficient for the time series to eliminate the self-intersection of the trajectory. I believe it is necessary to compute the fractal dimension.
You could also try Dataplore (http://dataplore.de) which provides a bunch of tools for nonlinear analysis, including recurrence plots, surrogate data, peak-to-peak intervals, correlation integral and dimension, global and local Lyapunov exponents, global and local transinformation of two time series and pointwise conditional coupling divergence. It can also help to find the appropriate parameters for you phase space (e.g. the delay or the embedding dimension).
If you are interested in fractal dimension i will recommend TISEAN package or OPENTSTOOL. The most commonly used fractal dimensions are correlation dimension, kaplan yorke dimension ( which is a consequence of Lyapunov exponent), hausdoff dimension amongst others. There are stand alone codes to use.
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