Coupled system
Quadratic interactions prevent unbounded linear error growth.
x′=σ(y−x), y′=x(ρ−z)−y, z′=xy−βz
The Lorenz 63 Model
A simple system revealing chaos and predictability limits
Three coupled nonlinear ODEs produce the iconic butterfly attractor and rapid separation of nearby trajectories.
watchone idea
→manipulateone example
→leave withone intuition
The essential idea: near-identical initial conditions can yield different paths while remaining on the same statistical attractor.
One Concept · One Example
The Lorenz 63 Model
Presented by Charlotte Moser · Coming soon
What to notice
- The standard parameters are σ=10, ρ=28, β=8/3.
- A 0.1% perturbation eventually changes the trajectory.
- Both paths retain the same double-lobed geometry.
The mathematical structure
Nearby starts
The slides compare x(0)=1 and x(0)=1.001.
||δx(t)|| grows before saturating on the attractor
Run two nearly identical Lorenz forecasts
Use the slides' initial conditions, then vary the perturbation or ρ. Compare time series, attractor geometry, and separation.
Lorenz 63 shows why deterministic equations can support only finite-horizon pathwise prediction.