Extensions
Multivariate extensions of recurrence plots were developed as cross recurrence plots and joint recurrence plots.
Cross recurrence plots consider the phase space trajectories of two different systems in the same phase space (Marwan & Kurths 2002):
The dimension of both systems must be the same, but the number of considered states (i.e. data length) can be different. Cross recurrence plots compare the simultaneous occurrences of similar states of two systems. They can be used in order to analyse the similarity of the dynamical evolution between two different systems, to look for similar matching patterns in two systems, or to study the time-relationship of two similar systems, whose time-scale differ (Marwan & Kurths 2005).
Joint recurrence plots are the Hadamard product of the recurrence plots of the considered sub-systems (Romano et al. 2004), e.g. for two systems and the joint recurrence plot is
In contrast to cross recurrence plots, joint recurrence plots compare the simultaneous occurrence of recurrences in two (or more) systems. Moreover, the dimension of the considered phase spaces can be different, but the number of the considered states has to be the same for all the sub-systems. Joint recurrence plots can be used in order to detect phase synchronisation.
Read more about this topic: Recurrence Plot
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