Regular Article

Synchronization patterns in Stuart–Landau networks: a reduced system approach

¹ Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
² Laboratoire des signaux et systèmes, CNRS, 3 rue Joliot Curie, 91192 Gif-sur-Yvette, France

^a e-mail: schoell@physik.tu-berlin.de

Received: 1 August 2018
Received in final form: 22 January 2019
Published online: 14 May 2019

Abstract

We study networks with coupled phase and amplitude dynamics. In particular, we investigate a ring of Stuart–Landau oscillators. For symmetry-conserving coupling we observe cluster synchronization. We show that the dimension of the dynamical system can be substantially reduced by projecting the system onto the subspace corresponding to the unstable eigenvalues of the linear part of the network dynamics.