title: Stable and transient multicluster oscillation death in nonlocally coupled networks.
abstract: In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multicluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation, which works well for large coupling ranges but fails for coupling ranges, which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.
authors.affiliation: Institut für Mathematik, Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Germany.
authors.forename: Isabelle
authors.initials: I
authors.lastname: Schneider
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
authors.forename: Marie
authors.initials: M
authors.lastname: Kapeller
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
authors.forename: Sarah
authors.initials: S
authors.lastname: Loos
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
authors.forename: Anna
authors.initials: A
authors.lastname: Zakharova
authors.affiliation: Institut für Mathematik, Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Germany.
authors.forename: Bernold
authors.initials: B
authors.lastname: Fiedler
authors.affiliation: Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany.
authors.forename: Eckehard
authors.initials: E
authors.lastname: Schöll