Cobweb plot

Construction of a cobweb plot of the logistic map y = 2.8 x (1-x), showing an attracting fixed point.
An animated cobweb diagram of the logistic map y = r x (1-x), showing chaotic behaviour for most values of r > 3.57.

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 technique was introduced in the 1890s by E.-M. Lémeray.[1] Using a cobweb plot, it is possible to infer the long term status of an initial condition under repeated application of a map.[2]

  1. ^ Lémeray, E.-M. (1897). "Sur la convergence des substitutions uniformes" (PDF). Nouvelles annales de mathématiques, 3e série. 16: 306–319.
  2. ^ Stoop, Ruedi; Steeb, Willi-Hans (2006). Berechenbares Chaos in dynamischen Systemen [Computable Chaos in dynamic systems] (in German). Birkhäuser Basel. p. 8. doi:10.1007/3-7643-7551-5. ISBN 978-3-7643-7551-5.