Recurrence plot: Difference between revisions

Revision as of 16:27, 5 December 2020

Revision as of 15:00, 7 April 2021

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Operationally the plot is drawn as follows:

(a) A certain time window <math>\vec{w} = <t_0, t_1, ...tt_2, ..., t_T></math> is chosen where any two successive time steps are separated by the time interval <math>\varepsilon</math>, and where the state <math>\vec{x}(t) </math> of the system is recorded for each time step, thus collecting the trajectory <math> \mathbf{X} = <\vec{x}(t_0t_1), \vec{x}(t_1t_2), ..., \vec{x}(t_T)> </math>.

(b) A 2D plot is created where the x-axis and y-axis both report <math>\vec{w}</math>, forming a <math>T \times T</math> lattice of little squares each with side measuring <math>\varepsilon</math>

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:<math>R(i,j) = \begin{cases} 1 &\text{if} \quad \| \vec{x}(i) - \vec{x}(j)\| \le \varepsilon \\ 0 & \text{otherwise}, \end{cases}</math>

where <math>i,j \in \{t_0, t_1, ...tt_2, ..., t_T\}</math>.

(d) The recurrence plot then visualises <math>\mathbf{D}_{T,T}</math> with a black little square of the lattice at coordinates <math>(i,j)</math> if <math>R(i,j)=1</math>, and a white little square if <math>R(i,j)=0</math>.