Maximal Lyapunov Exponent dialog box

 

Use this dialog box to calculate the maximal Lyapunov exponent for selected series. The maximal Lyapunov exponent measures the exponent of the rate at which nearby trajectories diverge in state space. A positive maximal Lyapunov exponent is a strong indication of deterministic chaos.

 

 

Input

Specifies the worksheet location of the input data for this operation.

 

Valid Input Range

Provides a reference to the extent of the data available in the currently active worksheet. Use this range as a guide for typing valid cell ranges in the Input Range box.

 

Input Range

Type in this box the range of cells that contain the data you want to use as input for this command.

 

Series in Rows

Check this box to specify that the data specified by the Input Range box is organized in rows as opposed to columns (the default).

 

Series Context

 

Single Series

Select this option to indicate that the data specified by the Input Range box represent individual series.

 

Multivariate

Select this option to indicate that the data specified by the Input Range box represent one multidimensional series.

 

Refer to Specifying Input Arguments for additional information on this subject.

 

Output

Specifies the worksheet location for placing the results of this operation.

 

New Workbook

Select this option to place the results of this operation in a new document workbook.

 

New Sheet

Select this option to place the results of this operation in a new worksheet.

 

Range Position

Select this option to place the results of this operation starting at the worksheet location specified in the box to the right of this option.

 

Plot

Check this box to plot the results of this operation.

 

Refer to Specifying Output Locations for additional information on this subject.

 

Method

Select the tab for the method you want to use to calculate the maximal Lyapunov exponent. The maximal Lyapunov exponent is calculated according to the method indicated by the active tab when you click the OK button. For example, if you select the Kantz tab and click OK, the Lyapunov exponent is calculated according to Kantz.

 

Refer to Kantz (1994) and Rosenstein, Collins & De Luca (1993) for additional information on the methods used for calculating the maximal Lyapunov exponent.

 

Min. Dimensions

Specifies the minimal embedding dimension at which the maximal Lyapunov exponent is calculated.

 

Max. Dimensions

Specifies the maximal embedding dimension at which the maximal Lyapunov exponent is calculated.

 

Time Delay

Specifies the time delay used between every dimensional component of the embedding.

 

Min. Neighborhood

Specifies the minimum number of neighbors that will be used for calculating the maximal Lyapunov exponent at every epsilon.

 

 

Iterations

Spacifies the number of iterations in time evolution.

 

Exclusion Window

Specifies the size of the Theiler exclusion window to avoid the inclusion of neighbors exhibiting temporal correlation.

 

Refer to the Space Time Separation dialog box and Theiler (1986) for additional information on temporal correlations.

 

Minimum Epsilon

Specifies the minimal state space distance at which calculation of the maximal Lyapunov exponent will take place.

 

Maximum Epsilon

Specifies the maximal state space distance at which calculation of the maximal Lyapunov exponent will take place.

 

Epsilon Steps

Specifies the number of steps between the Minimum Epsilon and the Maximum Epsilon at which calculation of the maximal Lyapunov exponent takes place.

 

OK

Closes the dialog box and carries out this operation.

 

Cancel

Closes the dialog box without carrying out this operation.

 

Sample Output