10.3 Multidimensional RQA

In the present example all relevant dimensions of the system have been ‘observed’ (see figure 10.2) and in such a case a multidimensional recurrence matrix can be constructed by considering each time series a state vector \(\vec{y_i}\) of the \(m\)-dimensional phase space of the system. Multidimensional RQA simply refers to recurrence quantification analysis based on such a multidimensional recurrence matrix. Figure 10.7 represents the RP based on the multidimensional recurrence matrix, of the 4 coupled differential equations. The threshold \(\varepsilon\) was chosen to yield 5% recurrent points.

Figure 10.7: A recurrence plot based on the multidimensional recurrence matrix of the coupled 4D system.

Calculating the recurrence measures is exactly the same