The problem with chaotic systems is that while the butterfly’s wingbeat may influence a hurricane, there is no way to predict such a thing in advance. Working with chaotic systems always involves uncertainty at all levels.
David Snowden’s Cynefin framework is a great simple tool for the sorts of responses that are appropriate for different sorts of complexity (though he doesn’t directly address all different types of chaotic systems, only the most obvious).
In terms of creating change, linear exponential systems are far more effective and manageable than truly chaotic ones, and all real systems have chaotic elements within them. So whatever we do we need to be in a dance with how the system responds to our inputs.
And welcome to the dance! 😉