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When N is set to an integer value, the position and momentum variables can be restricted to integers and the mapping becomes a mapping of a toroidial square grid of points onto itself. Such an integer cat map is commonly used to demonstrate mixing behavior with Poincaré recurrence utilising digital images. The number of iterations needed to ...
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 .
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
Print/export Download as PDF ... Holmes chaotic map Duffing equation: continuous: ... Shobu-Ose-Mori piecewise-linear map: discrete: real: 1: piecewise-linear ...
The nodes, labeled 1 through n, are each associated with the corresponding row/column of A. If entry a ji ≠ 0 then there is a directed edge from node i to node j with weight a ji . [ 3 ] In other words, the Coates graph for matrix A is the one whose adjacency matrix is the transpose of A .
The bifurcation diagram shows the forking of the periods of stable orbits from 1 to 2 to 4 to 8 etc. Each of these bifurcation points is a period-doubling bifurcation. The ratio of the lengths of successive intervals between values of r for which bifurcation occurs converges to the first Feigenbaum constant.
Using the diagram and summing the incident branches into x 1 this equation is seen to be satisfied. As all three variables enter these recast equations in a symmetrical fashion, the symmetry is retained in the graph by placing each variable at the corner of an equilateral triangle. Rotating the figure 120° simply permutes the indices.
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