Correlation Dimension

Contents

Exercise

1. Roessler system

1.1. Compute the three data series of the Roessler system for 10000 data points by using the Matlab's ODE function.

1.2. Use the TISEAN command c2 in order to calculate the correlation sum for an appropriate range of epsilon and several embedding dimensions using the x-component of the Lorenz system. Determine the correlation dimension by using a log-log plot of C2 over epsilon and plot the estimated correlation dimension as a function of the embedding dimension.

1.3. Add some noise to the x-component and estimate the correlation dimension again. What happens when we further increase the noise? Up to which noise level we can still estimate a proper value of the correlation dimension?

2. Try to estimate the correlation dimension for the data in the file ecg.dat.