## jrqa

Computes and plots the JRQA measures.

### Syntax

```
jrqa(x)
jrqa(x,y)
y=jrqa(x,y,m,t,e,w,ws)
y=jrqa(x,y,m,t,e,w,ws,lmin,vmin)
y=jrqa(x,y,m,t,e,w,ws,lmin,vmin,tw)
y=jrqa(x,y,m,t,e,[],'param1','param2',...)
```

### Description

Recurrence quantification analysis of joint-recurrence
with the first vector `x` and the second `y`.
The results can be plotted.

The input vectors can be multi-column vectors, where each column will be used as a component of the phase-space vector. However, if the first column is monotonically increasing, it will be used as an time scale for plotting.

### Parameters

Dimension `m`, delay `t`, the size of
neighbourhood `e`, the window size `w` and the
shift value `ws` are the first five numbers after
the data series; if `w=[]` then the whole plot will
be calculated. The minimal length of
diagonal and vertical structures can be specified
with `lmin` and `vmin` respectively
(default is 2).

As the last numeric parameter, the size of the Theiler window `tw` can
be specified (default is 1). This window excludes the recurrence points
parallel to the main diagonal from the analysis.

Further parameters can be used to switch between various methods of finding the neighbours of the phasespace trajectory, to suppress the normalization of the data and to suppress the GUI (useful in order to use this programme by other programmes).

Methods of finding the neighbours. | ||

'maxnorm' | - | Maximum norm. |

'euclidean' | - | Euclidean norm. |

'minnorm' | - | Minimum norm. |

'nrmnorm' | - | Euclidean norm between normalized vectors (all vectors have the length one). |

'rr' | - | Maximum norm, fixed recurrence rate. |

'fan' | - | Fixed amount of nearest neighbours. |

'inter' | - | Interdependent neighbours. |

'omatrix' | - | Order matrix. |

'opattern' | - | Order patterns recurrence plot. |

Normalization of the data series. | ||

'normalize' | - | Normalization of the data. |

'nonormalize' | - | No normalization of the data. |

Suppressing the GUI. | ||

'gui' | - | Creates the GUI and the output plot. |

'nogui' | - | Suppresses the GUI and the output plot. |

'silent' | - | Suppresses all output. |

Output | ||

y(:,1) | - | Recurrence rate. |

y(:,2) | - | Determinism. |

y(:,3) | - | Averaged diagonal length. |

y(:,4) | - | Length of the longest diagonal line. |

y(:,5) | - | Entropy of diagonal length. |

y(:,6) | - | Laminarity. |

y(:,7) | - | Trapping time. |

y(:,8) | - | Length of the longest vertical line. |

y(:,9) | - | Recurrence time of 1st type. |

y(:,10) | - | Recurrence time of 2nd type. |

Parameters not needed to specify.

### Limitations

For higher speed in output the whole matrix of the recurrence
plot is in the work space - this limits the application of long data
series. However, a solution for using long data series you can find
under the description for `crp`.

### Warning

The RQA measures may differ from those of the RQA programmes by Charles Webber Jr. For compatibility use a Theiler window of size one and ensure that the data are normalized before by the same distance which is used in the RQA programmes; e.g. normalize with the maximal phase space diameter, which can be estimated with the programme pss:

```
RQA=jrqa(100*x/pss(x,dim,lag,'euclidean'),dim,lag,e,[],[],l_min,v_min,1,...
'euclidean','nonormalize','silent')
```

### Examples

```
N=500; w=40; ws=10;
b=.4; a=.6; mu=.8:-0.7/N:.1;
% two mutually coupled logistic maps
for i=2:N,
a(i)=3.6*a(i-1)*(1-a(i-1));
b(i)=4*b(i-1)*(1-b(i-1))-mu(i)*a(i);
end
% coupling is obtained by higher RR and DET values
jrqa(a,b,1,1,.2,w,ws);
```

### See Also

### References

Trulla, L. L., Giuliani, A., Zbilut, J. P., Webber Jr., C. L.: Recurrence quantification analysis of the logistic equation with transients, Phys. Lett. A, 223, 1996.

Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J.: Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data, Phys. Rev. E, 66(2), 2002.

Romano, M., Thiel, M., Kurths, J., von Bloh, W.: Multivariate Recurrence Plots, Phys. Lett. A, 330, 2004.