PHASE SPACE EXPLORER
Stable spiral
+ Click to add a trajectory
x₁ · x₂
t = −20.00
Initial values are at t = 0
Trace–determinant plane
Click or drag to explore. Arrow keys fine-tune; hold Alt to skip snapping to boundaries.
Δ = τ²/4: repeated eigenvaluesτ = 0, Δ > 0: centersΔ = 0: zero eigenvalue
Fixed samples stay in place; the tracked pair follows the stable saddle direction continuously. Each point generates one representative matrix; matrices with the same trace and determinant can differ on the boundary curves.
Solution over time
x₁x₂x₃
System insight
EIGENVALUESTrace Determinant