What are good examples of applying dynamical systems in cognitive science? I'm a mathematics and physics student very much interested in cognitive science. Recently I've been hearing about "a new approach" in cognitive science via dynamical system theory. 


What are some good examples of using differential equations to model cognitive phenomena?
What papers would you recommend?
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:


  A highly illustrative example comes from the orientation behaviors of
  the common house ﬂy (Reichardt &amp; Poggio, 1976; Poggio &amp; Reichardt,
  1976). Flies orient toward moving objects, which they chase as part of
  their mating behavior. Detailed analysis revealed that the circuitry
  underlying this behavior forms a simple controller: a motion detection
  system fed by luminance changes on the ﬂy’s facet eye drives the ﬂight
  motor, generating an amount of torque that is a function of where on
  the sensory surface motion was detected. If the speck of motion is
  detected on the right, a torque to the right is generated. If the
  speck is detected on the left, a torque to the left is generated. The
  level of torque passes through zero when the speck is right ahead. The
  torque changes the ﬂight direction of the ﬂy, which in turn changes
  the location on the facet eye at which the moving stimulus is
  detected. Given the aerodynamics of ﬂies, the torque and its on-line
  updating generate an orientation behavior, in which the insect orients
  its ﬂight into the direction in which a moving stimulus is detected.