page_title: Recurrence quantification analysis
section_title: Example
hierarchical_section_title: Recurrence quantification analysis / Example
caption_attribution_description: English: A bifurcation diagram for the Logistic map: x n + 1 = r x n ( 1 &#x2212; x n ) {\displaystyle x_{n+1}=rx_{n}(1-x_{n})\,} The horizontal axis is the r parameter, the vertical axis is the x variable. The image was created by forming a 1601 x 1001 array representing increments of 0.001 in r and x. A starting value of x=0.25 was used, and the map was iterated 1000 times in order to stabilize the values of x. 100,000 x&#160;-values were then calculated for each value of r and for each x value, the corresponding (x,r) pixel in the image was incremented by one. All values in a column (corresponding to a particular value of r) were then multiplied by the number of non-zero pixels in that column, in order to even out the intensities. Values above 250,000 were set to 250,000, and then the entire image was normalized to 0-255. Finally, pixels for values of r below 3.57 were darkened to increase visibility.
context_page_description: Recurrence quantification analysis is a method of nonlinear data analysis for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory.
caption: Bifurcation diagram for the Logistic map.
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