Lyapunov exponents measure: rate of divergence of nearby trajectories in a dynamical system

How do tiny differences grow over time in chaotic systems?

Imagine you're planting seeds in a garden. If two seeds start just a millimeter apart, under certain conditions, they might end up miles apart after a while.

In our garden, the seeds' final distance apart shows how much they spread out. This spreading rate tells us how chaotic the garden's growth is.

Example

If seeds start 1mm apart and after a month they're 10km apart, the garden's growth is extremely chaotic.

Remember this

The Lyapunov exponent measures how quickly tiny differences grow, indicating chaos.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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