Recurrence plot: Difference between revisions

Revision as of 15:00, 7 April 2021

Revision as of 15:08, 7 April 2021

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(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>

(c) The data <math>\mathbf{X}</math> are used to compute a matrix <math>\mathbf{D}_{T,TR}</math> formed by binary elements recording the recurrence/non-recurrence of values <math>\vec{x}</math> through the binary function:

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

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where <math>i,j \in \{t_1, t_2, ..., t_T\}</math>.

(d) The recurrence plot then visualises <math>\mathbf{D}_{T,TR}</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>.

The visual appearance of a recurrence plot gives hints about the dynamics of the system. Caused by characteristic behaviour of the phase space trajectory, a recurrence plot contains typical small-scale structures, as single dots, diagonal lines and vertical/horizontal lines (or a mixture of the latter, which combines to extended clusters). The large-scale structure, also called ''texture'', can be visually characterised by ''homogenous'', ''periodic'', ''drift'' or ''disrupted''. For example, the plot can show if the trajectory is strictly periodic with period <math>T</math>, then all such pairs of times will be separated by a multiple of <math>T</math> and visible as diagonal lines.