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## Main Question or Discussion Point

What is the difference between nonlinearity and chaos, or is there a difference?

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What is the difference between nonlinearity and chaos, or is there a difference?

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Not all nonlinear systems of eqs are chaotic.

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As it stands, the shortest answer would be "they're not the same thing". Chaos is a different phenomenon to nonlinearity, but sometimes arises from it.

vanesch

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The definition of a chaotic system is:

- exponential divergence of initially close orbits (Liapunov instability)

- the state of the system remains in a compact space

Well, you cannot satisfy both with a linear system: in the case there is exponential divergence, at least one solution will become unbounded.

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