Synchronization of coupled Boolean phase oscillators.
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA and Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, Berlin D-10623, Germany.
David P
DP
Rosin
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA and Supélec, OPTEL Research Group, and LMOPS EA-4423, 2 Rue Edouard Belin, Metz F-57070, France.
Damien
D
Rontani
Department of Physics, Duke University, 120 Science Drive, Durham, North Carolina 27708, USA.
Daniel J
DJ
Gauthier