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Given your background and interest in modeling, I would highly recommend The Cambridge Handbook of Computational Psychology. The book provides an overview for several of the prominent modeling paradigms in cogsci, including dynamical systems, as well as many concrete examples--albeit most using other computational paradigms.

Dynamical systems, to my knowledge, are most used in the field of motor control. Though to be honest, dyn systems is not 'my' paradigm, and most of my knowledge comes from the aforementioned book.

In particular, the chapter "Dynamical Systems Approaches to Cognition" by G. Schoner gives this example that has always stuck in my mind: