Applications itérées et bifurcations

Application logistique, attracteur de Hénon, toile d’araignée et diagrammes de bifurcation.

About this tool

Discrete dynamical systems xn+1 = f(xn) on intervals or tori. Cobweb diagrams trace 1D orbits; phase portraits show 2D attractors; bifurcation and Lyapunov scans vary a control parameter.

Views

  • Iterate — time series of a coordinate (optional perturbed orbit overlay).
  • Cobweb — 1D map with diagonal guide (logistic, tent, …).
  • Torus heatmap — visit density on [0,1)×[0,1) for wrap maps (cat, baker, horseshoe).
  • Symbolic — binary (dyadic) or 4-symbol (horseshoe) coding strip.
  • Conjugate — logistic r=4 beside tent r=2 from the same x0 (topological chaos pair).

Period-doubling in the logistic map leads to the Feigenbaum route to chaos; positive Lyapunov exponent signals sensitive dependence.