Error growth
The linear unstable model isolates the amplification mechanism.
δu(t)=δu₀e^{λt}
Chaotic Systems
How tiny differences become large consequences
Chaos is deterministic, but positive error-growth rates make long-range trajectory prediction intrinsically fragile.
watchone idea
→manipulateone example
→leave withone intuition
The essential idea: a positive Lyapunov exponent turns small initial uncertainty into exponentially growing forecast error.
One Concept · One Example
Chaotic Systems
Presented by Charlotte Moser · Coming soon
What to notice
- Chaos does not require random forcing.
- Nearby trajectories first separate exponentially.
- A finite error threshold defines a predictability horizon.
The mathematical structure
Lyapunov exponent
A positive long-time growth rate signals sensitive dependence.
λ=limₜ→∞ t⁻¹ log(||δx(t)||/||δx₀||)
Measure a predictability horizon
Adjust the initial error and growth rate from the slides' exponential mechanism, then see when a forecast tolerance is crossed.
Tiny uncertainty becomes a practical prediction limit when dynamics amplify errors exponentially.