The entire justification of the biopsychosocial idea was systems theory, if you read Engel.
Chaos theory and associated math is hard systems theory. It has potential. The flip side is soft systems. Systems can be embraced without getting into mathematics.
One of the problems of math based systems theory is that it is very vulnerable to minute uncertainties in measurement and quantification. Add in some dynamics and the whole mathematical system becomes too variable to be precise. This is why climate modellers tweak hundreds of mathematical models and look for common patterns in outcomes. If a wide range of parameters give similar outcomes, then the model is considered to have some predictive value. The uncertainty is however high. For many situations I think a non-mathematical (actually it is based on maths, but graph theory not equations) approach suits many problems far more.
I've just got a copy of Engels paper now so I will try to read it over the next few days.
By mathematics I don't necessarily mean equations. I see logic and descrete mathematics (including graph theory) as important modelling tools that can be used to specify and simulate complex systems. What the mathematisation gives is a formalisation that tries to ensure concepts can be clearly expressed, understood and reasoned about. Finding the right conceptual framework (and hence formalisation) for a given problem can be hard and sometimes becomes the key to the correct understanding of a system.
I have problems with descriptive text where the meaning can be reinterpreted over the years and where vagueness in the arguments makes it hard to confirm or deny statements let alone check for the internal consistancy of an argument.