Applied Math Distinguished Lecture | Ian Stewart, Synchronisation in Feedforward Networks

MC 5501 

Speaker

Ian Stewart | University of Warwick, Department of Mathematics

Title

Synchronisation in Feedforward Networks

Abstract

In a network of dynamical systems, nodes are synchronous if they have identical time series. A periodic state is phase synchronous if this is the caseexcept for a phase shift. Both phenomena are controlled by balanced colorings, in which nodes are split into disjoint sets (colors), and nodeswith the same color have color-isomorphic inputs. We discuss joint work with David Wood (University of Warwick) on networks where some subnetwork ('central pattern generator') generates dynamics that feeds forward to the remainder of the network in a manner that naturally creates such patterns. A key issue is the stability of the resulting states.The main results concern Floquet and Liapunov stability of periodic statesto synchrony-breaking perturbations. Examples include 'toy' models of neurons and a hypothetical CPG for biped locomotion.