Search results
Results from the WOW.Com Content Network
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.
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 .
The Hénon map does not have a strange attractor for all values of the parameters a and b. 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.
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.
A compressor map is a chart which shows the performance of a turbomachinery compressor. This type of compressor is used in gas turbine engines, for supercharging reciprocating engines and for industrial processes, where it is known as a dynamic compressor. A map is created from compressor rig test results or predicted by a special computer program.
Graph of tent map function Example of iterating the initial condition x 0 = 0.4 over the tent map with μ = 1.9. In mathematics, the tent map with parameter μ is the real-valued function f μ defined by ():= {,}, the name being due to the tent-like shape of the graph of f μ.
An example would be showing one variable as a choropleth map, with another variable shown as proportional symbols on top of the choropleth. A correlated symbol map represents two or more variables in the same thematic map layer, using the same visual variable , designed in such a way as to show the relative combination of the two variables.
Causal maps have been used since the 1970’s by researchers and practitioners in a range of disciplines from management science [4] to ecology, [5] employing a variety of methods. They are used for many purposes, for example: As sketch diagrams to summarise causal links [6] As tools to understand how decisions are made [7]