Intermittent interactions: Dynamics of oscillator networks with dead zones
Christian Bick
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.)