Abstract. 
Whether two nodes in a network of dynamical units interact may depend on
their states. For example, after a spike, neurons typically have a 
refractory period where they are desensitized to further input before 
they can produce another action potential. We investigate the dynamics 
of coupled oscillator networks where the coupling functions have "dead 
zones" (regions without interaction). These induce an effective coupling 
structure that depends on the state of the network. We analyze the 
interplay between dynamics and the evolving coupling structure and find 
solutions where units decouple and recouple as time evolves. These 
state-dependent dynamical systems relate to "asynchronous networks," a 
framework to describe dynamical systems with time-varying connectivity 
and typically nonsmooth dynamics. (This is joint work with P. Ashwin, M. 
Field, C. Poignard.)