Time: 9h30, Tuesday, October 29, 2019
Location: Room 302, Building A5, Institute of Mathematics
Abstract: Many systems can be seen as network of interacting dynamical units. The collective network dynamics of all units - for example, whether different units synchronize or not - depends on the network structure (what node is coupled to what other unit) and the interactions (how does one unit influence another unit). Importantly, interactions may depend on the state of the units. 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. Here, 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.)