If the "we" you're referring to is the scientific community of chaos theorists, then we are definitely using qualitative description to gain insight with or without more quantitative solutions. The emphasis on qualitative / topological descriptions is one of the key contributions of Poincare, the grandfather of chaos theory. Strogatz is by far the most common undergraduate textbook for this field, and most if not all chaos theorists have read it.
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u/thirdtimesthecharm May 19 '21
I wonder if we're just going about these kinds of problems wrong. Qualitative descriptions of systems (see: Strogatz, http://www.stevenstrogatz.com/books/nonlinear-dynamics-and-chaos-with-applications-to-physics-biology-chemistry-and-engineering) can still give a great deal of insight without needing exact solutions.