First line of the Wikipedia page is fine: "In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input."

Scientific American's typical reader surely understands a) the concept of a function b) the concept of proportionality.

It's fine to say that nonlinear systems are difficult to analyze, or have a reputation for being difficult to analyze. But it's bad practice for a science communicator even to run the risk of giving people the impression that the difficulty is part of the meaning (definition) of the word.