An Isaac Newton Institute Workshop

Theory and Applications of Coupled Cell Networks

Network topology and delay-induced oscillator death

Author: Fatihcan M. Atay (Max Planck Institute for Mathematics in the Sciences)

Abstract

The fact that transmission delays can suppress oscillatory behavior of coupled systems has recently attracted attention in diverse scientific fields. The implications for biological systems are easily appreciated if one considers the possibility of cessation of oscillations in a group of cardiac cells or neurons as a result of delayed coupling. The relation of this phenomenon to coupling topology was so far unknown. In this talk, I will consider systems near Hopf bifurcation as oscillators, and give a complete characterization of delay-induced stability in terms of the spectrum of the graph Laplacian, for both directed or undirected networks.