Geodesic
Collective synchronization of classical and quantum oscillators
Seung-Yeal Ha1 ; Dongnam Ko1 ; Jinyeong Park2 ; Xiongtao Zhang1
1Seoul National University, South Korea
2Universidad de Granada, Spain
EMS surveys in mathematical sciences, Tome 3 (2016) no. 2, pp. 209-267

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DOI

Synchronization of weakly coupled oscillators is ubiquitous in biological and chemical complex systems. Recently, research on collective dynamics of many-body systems has been received much attention due to their possible applications in engineering. In this survey paper, we mainly focus on the large-time dynamics of several synchronization models and review state-of-art results on the collective behaviors for synchronization models. Following a chronological order, we begin our discussion with two classical phase models (Winfree and Kuramoto models), and two quantum synchronization models (Lohe and Schrödinger–Lohe models). For these models, we present several sufficient conditions for the emergence of synchronization using mathematical tools from dynamical systems theory, kinetic theory and partial differential equations in a unified framework.
DOI : 10.4171/emss/17
Classification : 70-XX, 92-XX
Mots-clés : Kuramoto oscillators, large-time dynamics, Lohe oscillators, synchronization and Winfree oscillators

Seung-Yeal Ha  1   ; Dongnam Ko  1   ; Jinyeong Park  2   ; Xiongtao Zhang  1

1 Seoul National University, South Korea
2 Universidad de Granada, Spain 
Seung-Yeal Ha; Dongnam Ko; Jinyeong Park; Xiongtao Zhang. Collective synchronization of classical and quantum oscillators. EMS surveys in mathematical sciences, Tome 3 (2016) no. 2, pp. 209-267. doi: 10.4171/emss/17
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     title = {Collective synchronization of classical and quantum oscillators},
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     doi = {10.4171/emss/17},
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