ESE 2100 · Simulation 3
Bifurcation Lab
A one-dimensional engine for continuous-time systems
ẋ = f(x, μ) . Drag μ, drop a state, and watch equilibria
appear, collide, exchange stability, or split.
Bifurcation diagram · x versus μ
parameter μ
Sweep μ →
Hysteresis loop
Reset particle
Vector field · f(x; μ) and the phase line
How to read it
Solid teal branches are attracting equilibria; dashed coral branches are repelling.
The gold line is the current μ. Click the vector-field plot to drop a particle.
Arrow keys nudge μ; space starts a slow sweep.
Why one dimension
In a 1-D continuous-time system the only generic bifurcations of equilibria are
saddle-node, transcritical, and pitchfork. A Hopf bifurcation needs a 2-D phase
plane — saved for later. Discrete time (maps) can period-double; this lab stays
with flows ẋ = f(x, μ).