- journal article metadata
European Mathematical Society Publishing House
2016-11-18 16:39:54
EMS Surveys in Mathematical Sciences
EMS Surv. Math. Sci.
EMSS
2308-2151
2308-216X
General
10.4171/EMSS
http://www.ems-ph.org/doi/10.4171/EMSS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
3
2016
2
Collective synchronization of classical and quantum oscillators
Seung-Yeal
Ha
Seoul National University, SEOUL, SOUTH KOREA
Dongnam
Ko
Seoul National University, SEOUL, SOUTH KOREA
Jinyeong
Park
Universidad de Granada, GRANADA, SPAIN
Xiongtao
Zhang
Seoul National University, SEOUL, SOUTH KOREA
Kuramoto oscillators, large-time dynamics, Lohe oscillators, synchronization and Winfree oscillators
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.
Mechanics of particles and systems
Biology and other natural sciences
209
267
10.4171/EMSS/17
http://www.ems-ph.org/doi/10.4171/EMSS/17