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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<ref>{{cite
|author1=N. Marwan |author2=J. Kurths | title=Nonlinear analysis of bivariate data with cross recurrence plots
| journal=Physics Letters A
| volume=302
| issue=5–6
| year=2002
| doi=10.1016/S0375-9601(02)01170-2
| pages=299-307
|bibcode = 2002PhLA..302..299M
| s2cid=8020903 }}</ref>:
:<math>\mathbf{CR}(i,j) = \Theta(\varepsilon - \| \vec{x}(i) - \vec{y}(j)\|), \quad \vec{x}(i),\, \vec{y}(i) \in \mathbb{R}^m, \quad i=1, \dots, N_x, \ j=1, \dots, N_y.</math>
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 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<ref>{{cite
|author1=N. Marwan |author2=J. Kurths | title=Line structures in recurrence plots
| journal=Physics Letters A
| volume=336
| issue=4-5
| year=2005
| doi=10.1016/j.physleta.2004.12.056
| pages=349–357
|bibcode = 2005PhLA..336..349M
| s2cid=931165 }}</ref>.
Joint recurrence plots are the [[Matrix product#Hadamard product|Hadamard product]] of the recurrence plots of the considered sub-systems
|author1=M. C. Romano |author2=M. Thiel |author3=J. Kurths |author4=W. von Bloh
| title=Multivariate Recurrence Plots
| journal=Physics Letters A
| volume=330
| issue=3-4
| year=2004
| doi=10.1016/j.physleta.2004.07.066
| pages=214–223
|bibcode = 2004PhLA..330..214R
| s2cid=5746162 }}
</ref>, e.g. for two systems <math>\vec{x}</math> and <math>\vec{y}</math> the joint recurrence plot is
:<math>\mathbf{JR}(i,j) = \Theta(\varepsilon_x - \| \vec{x}(i) - \vec{x}(j)\|) \cdot \Theta(\varepsilon_y - \| \vec{y}(i) - \vec{y}(j)\|), \quad \vec{x}(i) \in \mathbb{R}^m, \quad \vec{y}(i) \in \mathbb{R}^n,\quad i,j=1, \dots, N_{x,y}.</math>
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