Stability of amplitude chimeras in oscillator networks
1 Institut für Theoretische Physik, Technische Universität Berlin - Hardenbergstraße 36, 10623 Berlin, Germany
2 Queen Mary, University of London, School of Mathematical Sciences - Mile End Road, London E1 4NS, UK
Received: 7 November 2016
Accepted: 20 February 2017
We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase-space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size N = 12 exhibiting amplitude chimeras.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 89.75.-k – Complex systems
© EPLA, 2017