Asymmetric dynamic interaction shifts synchronized frequency of coupled oscillators

Abstract

interacting dynamic agents can often exhibit synchronization. it has been reported that the rhythm all agents agree on in the synchronized state could be different from the average of intrinsic rhythms of individual agents. Hinted by such a real-world behavior of the interaction-driven change of the average phase velocity, we propose a modified version of the Kuramoto model, in which the ith oscillator of the phase φ i interacts with other oscillator j only when the phase difference j φ − i φ is in a limited range [−βπ, απ]. From extensive numerical investigations, we conclude that the asymmetric dynamic interaction characterized by β ≠ α leads to the shift of the synchronized frequency with respect to the original distribution of the intrinsic frequency. We also perform and report our computer-based synchronization experiment, which exhibits the expected shift of the synchronized frequency of human participants. in analogy to interacting runners, our result roughly suggests that agents tend to run faster if they are more influenced by runners ahead than behind. We verify the observation by using a simple model of interacting runners.

The Sakaguchi-Kuramoto Model in Presence of Asymmetric Interactions That Break Rotational Symmetry.

“…Considering symmetric interaction in the dynamics is only an approximation that may simplify theoretical analysis, but which may fail to capture important phenomena occurring in real systems. For example, asymmetric interaction leads to novel features such as families of traveling wave states [13,14], glassy states and super-relaxation [15], and so forth, and has been invoked to discuss coupled circadian neurons [16], dynamic interactions [17], etc. A generalization of the Kuramoto model (1) that accounts for asymmetric interaction is the so-called Sakaguchi-Kuramoto (SK) model, with the dynamics described by the equation of motion [18] dθ…”

The Sakaguchi-Kuramoto model in presence of asymmetric interactions that break phase-shift symmetry

“…Considering sym-metric interaction in the dynamics is only an approximation that may simplify theoretical analysis, but which may fail to capture important phenomena occurring in real systems. For example, asymmetric interaction leads to novel features such as families of travelling wave states 13,14 , glassy states and super-relaxation 15 , and so forth, and has been invoked to discuss coupled circadian neurons 16 , dynamic interactions 17,18 , etc. A generalization of the Kuramoto model (1) that accounts for asymmetric interaction is the so-called Sakaguchi-Kuramoto model, with the dynamics described by the equation of motion 19 dθ…”