Wave propagation of phase difference in coupled oscillator arrays

2016 ◽  
pp. 133-162 ◽  
Author(s):  
Masayuki Yamauchi Yamauchi ◽  
Yoshihito Todani Todani ◽  
Syohei Fujimoto Fujimoto
Keyword(s):  
Wave Propagation ◽  
Phase Difference ◽  
Coupled Oscillator ◽  
Oscillator Arrays

Frequency Modulated Coupled Oscillator Arrays

2001 ◽  
Author(s):  
Ragip Ispir ◽  
Akira Miyata ◽  
Kazunari Kawahata ◽  
Masao Ida ◽  
Yohei Ishikawa
Keyword(s):  
Coupled Oscillator ◽  
Oscillator Arrays

Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays

2000 ◽  
Vol 61 (5) ◽  
pp. 5080-5090 ◽  
Author(s):  
Kenneth S. Fink ◽  
Gregg Johnson ◽  
Tom Carroll ◽  
Doug Mar ◽  
Lou Pecora
Keyword(s):  
Coupled Oscillators ◽  
Coupled Oscillator ◽  
Oscillator Arrays

STABILITY OF SYNCHRONIZATION IN NETWORKS OF DIGITAL PHASE-LOCKED LOOPS

1995 ◽  
Vol 05 (04) ◽  
pp. 983-990 ◽  
Author(s):  
GUILLERMO GOLDSZTEIN ◽  
STEVEN H. STROGATZ
Keyword(s):  
Linear Stability ◽  
Phase Locked Loops ◽  
Explicit Formulas ◽  
Coupled Oscillator ◽  
Transient Time ◽  
Digital Phase ◽  
Digital Phase Locked Loops ◽  
Oscillator Arrays ◽  
Specific Phase

We analyze the linear stability of the synchronized state in networks of N identical digital phase-locked loops. These are pulse-coupled oscillator arrays in which the frequency (rather than the phase) of each oscillator is updated discontinuously whenever that oscillator reaches a specific phase in its cycle. Three different coupling configurations are studied: one-way rings, two-way rings, and globally coupled arrays. In each case we obtain explicit formulas for the transient time to lock, the critical gain at which the synchronized state loses stability, and the period of the bifurcating solution at the onset of instability. Our results explain the numerical observations of de Sousa Vieira, Lichtenberg, and Lieberman.

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