Propagation and reflection of phase differences on a lattice of coupled oscillators

Abstract

In this study, the propagation phenomena of phase differences under 180 degrees between adjacent oscillators can be observed on coupled oscillators by inductors as a lattice. The phenomenon can be observed in transient states. We call the phenomenon "phase-waves." We explain the propagation and the reflection mechanisms of the phase-waves using frequencies of each oscillator and phase differences between adjacent oscillators. Furthermore, we discover to observe an other wave on the above same circuit. The wave can be observed in steady states. We call the wave "phase-inversion wave." We clarify a region which can be observed the phase-inversion waves.

Analysis of Phase-Inversion Waves in In-and-Anti-Phase Synchronization on Coupled Van der Pol Oscillators as a 2D Lattice by Using an Actual Circuit

“…In our previous study, we have been observing synchronization phenomena on a ladder networks and 2D lattice networks of coupled van der Pol oscillators [3]. We observed not only in-phase, anti-phase or in-and-anti-phase synchronization of steady states but also phenomena of propagating phase differences.…”

Propagation mechanism of phase-inversion wave in 2D lattice oscillators and their application to prediction of time-series data

“…2 Φ (6,1)(7,1) starts to increase from 0 degree to 180 degrees, because f (7,1) changes from f in−in to f in−anti . 3 f (6,1) starts to increase from f in−in to f in−anti because Φ (6,1)(7,1) increases toward 180 degrees. Instantaneous frequency f (6,2) of an adjacent oscillator starts to increase at same time by propagating a phase-inversion wave in the adjacent column.…”

“…3 f (6,1) starts to increase from f in−in to f in−anti because Φ (6,1)(7,1) increases toward 180 degrees. Instantaneous frequency f (6,2) of an adjacent oscillator starts to increase at same time by propagating a phase-inversion wave in the adjacent column. Therefore, Φ (6,1)(6,2) is fixed as around 0 degrees.…”

“…On the lattice shape system, the phasewaves and the phase-inversion waves were discovered[6], [7]. Propagation and reflection mechanisms of the phase-waves were clarified [6]. Moreover, we developed a prediction method of time-series data using the lattice shape system.…”

“…The propagation and reflection mechanisms of the phase-waves and the phase-inversion waves were clarified [4], [5]. On the lattice shape system, the phasewaves and the phase-inversion waves were discovered [6], [7]. Propagation and reflection mechanisms of the phase-waves were clarified [6].…”