Recurrence plot: Difference between revisions

Revision as of 14:36, 6 September 2022

Revision as of 14:36, 6 September 2022

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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> \quad \| \cdotscdot \|</math> is a norm and <math>\varepsilon</math> the recurrence threshold. The recurrence plot visualises <math>\mathbf{R}</math> with coloured (mostly black) dot at coordinates <math>(i,j)</math> if <math>R(i,j)=1</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.