Rephrase "growth/decrease rate"

You ask, "Is there any way to condense it into one word? ("change" doesn't seem appropriate) or else rephrase the whole sentence?"

I would take the latter approach. You might try something like:

The Maximal Lyapunov Exponent characterizes the average rate at which a system's local uncertainty either grows or decreases over time.

This captures the idea that the rate is not merely variable, though if you need to be more clear about that idea, it might be better presented in a second sentence.

The Maximal Lyapunov Exponent characterizes a system's average local change rate of uncertainty.

I see no reason to discount the word change, even when applied to this area of science. Why obfuscate your meaning with jargon?

How about "decay" instead of decrease? Or maybe reduction in place of decrease. Fluctuation could be used in place of both.