GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS OF CARDIOVASCULAR DATA

|LEVEL 0| |HOMEPAGE|

Average exponential rates of divergence of initially close orbits in the phase space.

Let's consider two points in the phase-space, x and x', which are very close at time 0. They generate orbits in the space, and if the system has attracting fixed or periodic points, the distance between orbits will diminish asymptotically with time. By contrast, if the system is chaotic, two initially close orbits will tend to diverge (see figure).

The mean exponential rate of divergence of initially close orbits is measured by the Lyapunov exponents (one exponent for each direction of the phase-space axes). The sign of the Largest Lyapunov Exponent, LLE, allows to determine if the system is characterized by chaotic dynamics. If LLE is greater than 0, then nearby orbits diverge exponentially at least in one direction, and this implies a sensitive dependence of the system on initial conditions.

Ganz RE, Lenz C (1996) A program for the user-independent computation of the correlation dimension and the largest Lyapunov exponent of heart rate dynamics from small data sets, Comput Methods Programs Biomed

Links: For Source Code, Tutorials and Examples, see
TISEAN Nonlinear Time Series Analysis by R.Hegger, H.Kantz,T.Schreiber