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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.
An example is the bifurcation diagram of the logistic map: + = (). The bifurcation parameter r is shown on the horizontal axis of the plot and the vertical axis shows the set of values of the logistic function visited asymptotically from almost all initial conditions.
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 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.
In the Poincaré section S, the Poincaré map P projects a point x onto the point P(x). Let (R, M, φ) be a global dynamical system, with R the real numbers, M the phase space and φ the evolution function. Let γ be a periodic orbit through a point p and S be a local differentiable and transversal section of φ through p, called a Poincaré ...
The tent map with parameter μ = 2 and the logistic map with parameter r = 4 are topologically conjugate, [1] and thus the behaviours of the two maps are in this sense identical under iteration. Depending on the value of μ, the tent map demonstrates a range of dynamical behaviour ranging from predictable to chaotic.
To plot any dot from its spherical coordinates (r, θ, φ), where θ is inclination, the user would: move r units from the origin in the zenith reference direction (z-axis); then rotate by the amount of the azimuth angle (φ) about the origin from the designated azimuth reference direction, (i.e., either the x– or y–axis, see Definition ...
Comet plot : A two- or three-dimensional animated plot in which the data points are traced on the screen. Contour plot : A two-dimensional plot which shows the one-dimensional curves, called contour lines on which the plotted quantity q is a constant. Optionally, the plotted values can be color-coded.