What ODE-based models model growth economics?

Hi all,

This question popped up, but I don't quite know where to start in exploring it.

I was reading a paper on the ODE modeling of seasonality of epidemics, and the thought came to mind, what progress has there been in modeling growth economics with ODEs? Specifically, what ODE-based models attempt to predict the future growth of an economy, and more importantly, have there been any attempts at modeling the feedback loop between culture (Or people's behaviors) and economic conditions, instead of treating culture as this external factor in the models?

For context, I've been taking a class on nonlinear dynamics and chaos, with a focus on the textbook of the same name by Steven Strogatz, but there have been surprisingly few economics analogies, though I speculate it has to do with the difference between deterministic chaos vs. probabilistic modeling.