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Lesson 09
Lesson 09
Competing Stable States
The same rules can lead to different stable outcomes.
Some systems can settle into more than one stable arrangement. The final state may depend on the starting condition, past disturbances and the path taken through the controls.
Currently: State A
h = 0.00 · x = -1.00
Live explanation
What is happening?
The system is stable in State A.
Controls
Shape the landscape
0.00
0.50
0.20
What to notice
- More than one stable state can exist.
- Small disturbances may not cause switching.
- A sufficiently large disturbance can cross the unstable region.
- History can affect the current outcome.
- Reversing a control does not always reverse the state immediately.
Show the maths
Optional — the intuition already covers the important ideas.
V(x) = a x⁴ − b x² − h x
The shape contains two stable valleys separated by an unstable region. The bias h tilts the landscape and eventually removes one of the valleys.
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