## Momentary largest Lyapunov exponent

Purpose

Description

Macro Synopsis

Modules

Related Functions

### Purpose

Calculate the local largest Lyapunov exponent of a time series using a slided window

### Description

Lyapunov exponents quantify the rate of divergence of trajectories along various directions. "Momentary largest Lyapunov exponent" calculates the local largest Lyapunov exponents of a time series by means of a sliding window. The data sequence containing the exponents is returned as a signal.

Parameters of this function are

- the embedding dimension m,
- the number M of neighbours taken into account in phase space,
- the degree
`pd` of the fitting polynome,
- the window size N as number of samples and
- the number
`nsteps` of local largest Lyapunov exponents to be calculated.

**Warning:** *Phase space calculations on long signals are computationally very expensive, and can lead to large response times of the program. Try to use small radii and low embedding dimensions if possible.*

### Macro Synopsis

`y = MomLLE(x,m,M,pd,N,nsteps);`

signal x,y;

int m,M,pd,N,nsteps;

### Modules

Nonlinear

### Related Functions

Largest Lyapunov exponent (LLE), Lyapunov spectrum,
Correlation dimension, Correlation integral,
Pointwise correlation dimension (PD2), Pointwise correlation integral.