Berlin 2018 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 19: Chimera states: symmetry-breaking in dynamical networks (joint session DY/SOE)

SOE 19.4: Talk

Thursday, March 15, 2018, 10:45–11:00, BH-N 128

Symmetry-Broken Amplitude- and Phase-Locking in Two Identical Symmetrically Coupled Stuart-Landau Oscillators — •André Röhm, Isabelle Schneider, and Kathy Lüdge — Institut für Theoretische Physik, TU Berlin

In the model system of two instantaneously and symmetrically coupled identical Stuart-Landau oscillators we demonstrate that there exist stable solutions with symmetry-broken amplitude- and phase-locking. Similar to Chimera States, these states are a simple and approachable example of symmetry-breaking in oscillatory systems. They are characterized by a non-trivial fixed phase and amplitude relationship between both oscillators, while simultaneously maintaining perfectly harmonic oscillations of the same frequency. This is despite the fact, that we do not employ a symmetry-breaking coupling. These states have potential applications as bistable states for switches in a wide array of coupled oscillatory systems.

While some of the surrounding bifurcations have been previously described, we present the first detailed analytical and numerical description of these states and present analytically and numerically how they are embedded in the bifurcation structure of the system, arising both from the in-phase as well as the anti-phase solutions. The dependence of both the amplitude and the phase on parameters can be expressed explicitly with analytic formulas. As opposed to previous reports, we find that these symmetry-broken states are stable, which can we can show analytically.