For Students · Bifurcation Diagram
Bifurcation Diagram for a differential equation
Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a differential equation live below — adjust the inputs and watch it respond, right in your browser.
Bifurcation DiagramLive
logistic map · route to chaos
Controls
The logistic map xₙ₊₁ = r·xₙ(1−xₙ) doubles its period again and again as r grows, then dissolves into chaos near r ≈ 3.57 — with windows of order inside.
Presets
Data Inspector
Mapr·x(1−x)
Chaos onsetr ≈ 3.57
Feigenbaum δ4.669
Governing equation
Reading this result: Past r ≈ 3.57 the branches blur into chaos, yet pale vertical windows remain where periodic order suddenly returns.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
Also for:ResearchersEducatorsEngineersHobbyists & MakersK-12 StudentsFirst RespondersGeneral version →
More with Bifurcation Diagram
Bifurcation Diagram for compound interestBifurcation Diagram for a population curveBifurcation Diagram for a loan payoffBifurcation Diagram for a logistic mapBifurcation Diagram for a Fibonacci sequenceBifurcation Diagram for a fractal treeBifurcation Diagram for a Fourier seriesBifurcation Diagram for a Taylor approximation
Frequently asked questions
- Is this good for students?
- Yes — this version of "Bifurcation Diagram for a differential equation" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.