## Conditional coupling divergence (PCCD)

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Pointwise conditional coupling divergence (PCCD)

### Description

The conditional coupling convergence/divergence is a dynamic
coupling measure that can help investigating more complex and
instationary systems.

The basic idea behind the concept of conditional coupling divergence
is that two points being neighbours in the common phase space of the
two systems, stay close to each other after a short step in time
, if the systems are coupled.
Thus the Conditional coupling divergence (PCCD) is defined as the probability of two points lying in
the common phase space segment of radius r around a reference
trajectoy, both at a starting time and after k time
steps .

"Conditional coupling divergence (PCCD)" has the following parameters:

- delay parameter
`tau` (no. of samples) for phase space reconstruction,
- embedding dimension m,
- relative shift
`delta` of 2nd signal (as no. of samples),
- number k of evolution steps,
- relative radius r,
- counting
`mode`, either
- "Divergence (PCCD)" (0) or
- "Convergence (PCCC)" (1) and

- the normalization flag
`norm`, which is either
- "No" (0) if not, or
- "Yes" (1) if a normalization is to be performed.

Note that since this function operates on 'pure' time series, scales and shifts of the given signals do not affect the result.

### Macro Synopsis

`y = PCCD([x1,x2],tau,m,delta,k,r,mode,norm);`

signal x1,x2,y;

int tau,m,delta,k;

float r;

option mode,norm;

### Modules

Nonlinear

### Related Functions

Delta test,
Mutual cross information, Pointwise transinformation,
Post event scan, Synchronicity histogram, Transinformation.

### References

Vandenhouten [21]