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English: A bifurcation diagram for the Logistic map: + = The horizontal axis is the r parameter, the vertical axis is the x variable. A starting value of x=0.25 was used, and the map was iterated 1000 times in order to stabilize the values of x. 1,000,000 x -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.
A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.
Illustration showing how the rows of an UpSet plot correspond to the segments of a Venn diagram. An UpSet plot showing three sets, and the corresponding venn diagram. UpSet plots visualize intersections between sets in a matrix. In a vertical UpSet plot, the columns of the matrix correspond to the sets, the rows correspond to the intersections.
A two-dimensional Poincaré section of the forced Duffing equation. In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
For example, when one point is plotted for r, it is a fixed point, and when m points are plotted for r, it corresponds to an m-periodic orbit. When an orbital diagram is drawn for the logistic map, it is possible to see how the branch representing the stable periodic orbit splits, which represents a cascade of period-doubling bifurcations.
Nassi-Shneiderman diagrams and Drakon-charts are an alternative notation for process flow. Common alternative names include: flow chart, process flowchart, functional flowchart, process map, process chart, functional process chart, business process model, process model, process flow diagram, work flow diagram, business flow diagram. The terms ...
For example, by keeping b fixed at 0.3 the bifurcation diagram shows that for a = 1.25 the Hénon map has a stable periodic orbit as an attractor. Variation of 'b' showing the Bifurcation diagram. The boomerang shape is further drawn in bold at the top. Initial coordinates for each cross-section is (0, -0.2). Achieved using Python and Matplotlib.
An animated cobweb diagram of the logistic map = (), showing chaotic behaviour for most values of >. A cobweb plot , known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions , such as the logistic map .