Investigation Methods



ITEM Calculation of Lyapunov Exponents
Two methods are available: For maps, hybrid maps, CMLs, ODEs, hybrid ODEs, DDEs and hybrid DDEs:
ITEM Calculation of Poincaré sections
Several methods are available:
ITEM Symbolic image analysis

Several methods are available to investigate the global structures of dynamical systems:

All methods are based on the theoretical works of Prof. George Osipenko of the St. Petersburg State Polytechnical University (SPbSPU) and are developed in cooperation with him.

ITEM Box counting

Calculation of:
ITEM Period analysis
(For dynamical systems discrete in time)

Determination of: Attractors usually will be saved as time series and - for single-dimensional discrete maps - as a file containing the graphical iteration data.
ITEM Region analysis (based on Period analysis)
(For dynamical systems discrete in time)

Determination of:
ITEM Cobweb diagrams (based on Period analysis)
(For one-dimensional dynamical systems discrete in time)

The orbit data will be saved as time series containing the graphical iteration data.
ITEM Spectral analysis (based on the Fast Fourier Transform (FFT) of the FFTW library)

Calculation of the:
ITEM Principal component analysis
For multi-dimensional signals:
ITEM Symbolic sequence analysis

There are three possibilities to generate symbolic sequences based on: Depending on the computed symbolic sequences the following values will be calculated:
ITEM General trajectory analysis

Saving of:
ITEM Conditions checker

This method performs checks for some conditions and saves the time and the length of the trajectory from the beginning of the iteration, until a condition is fulfilled for the first time. The following conditions are implemented:
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Last modified: 2005-04-25    Contact: AnT