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DY: Fachverband Dynamik und Statistische Physik

DY 14: Focus Session: Chimera states: symmetry-breaking in dynamical networks (joint session DY/ BP)

DY 14.2: Hauptvortrag

Dienstag, 17. März 2015, 10:00–10:30, BH-N 243

Hysteretic transitions and chaotic chimera states in networks of Kuramoto oscillators with inertia — •Simona Olmi — CNR - Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy — INFN sez. Firenze, Sesto Fiorentino, Italy

We report finite size numerical investigations and mean field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine for a Gaussian distribution of the frequencies the transition from incoherence to coherence for increasingly large system size and inertia. For sufficiently large inertia the transition is hysteretic and within the hysteretic region clusters of locked oscillators of various sizes and different levels of synchronization coexist. A modification of the mean field theory developed by Tanaka, Lichtenberg, and Oishi [Physica D, 100 (1997) 279] allows to derive the synchronization profile associated to each of these clusters. By increasing the inertia the transition becomes more complex, and the synchronization occurs via the emergence of clusters of whirling oscillators. The presence of these groups of coherently drifting oscillators induces oscillations in the order parameter. We have shown that the transition remains hysteretic even for randomly diluted networks up to a level of connectivity corresponding to few links per oscillator. Finally an extension to a system of two symmetrically coupled networks of Kuramoto oscillators with inertia is reported. In this system the existence and the dynamical properties of novel chaotic chimera states are investigated, concentrating both on the microscopic dynamics and the macroscopic behavior.