Bob Rink

• The hidden symmetries of network dynamics
  Bob Rink
  Networks of coupled nonlinear dynamical systems often display unexpected phenomena. They may for example synchronise. This form of collective behaviour occurs when the agents of the network behave in unison. An example is the simultaneous firing of neurons. An elaborate theory for synchrony was developed by Golubitsky and coworkers. This theory was recently reformulated by DeVille and Lerman. They show that the patterns of synchrony of network systems are determined by so-called graph fibrations.
  In this talk I will show how graph fibrations also impact the global dynamics of networks. They are for example responsible for the unusual character of certain synchrony-breaking bifurcations. These bifurcations are forced by self-fibrations of a high dimensional lift of the network. This observation implies that networks are nothing but unusual examples of equivariant dynamical systems, and can be understood with the help of semigroup theory, representation theory and techniques from equivariant dynamical systems theory.
  This is joint work with Jan Sanders and Eddie Nijholt.