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Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model
The collective dynamics in populations of magnetic spin torque oscillators
(STO) is an intensely studied topic in modern magnetism. Here, we show that
arrays of STO coupled via dipolar fields can be modeled using a variant of the
Kuramoto model, a well-known mathematical model in non-linear dynamics. By
investigating the collective dynamics in arrays of STO we find that the
synchronization in such systems is a finite size effect and show that the
critical coupling-for a complete synchronized state-scales with the number of
oscillators. Using realistic values of the dipolar coupling strength between
STO we show that this imposes an upper limit for the maximum number of
oscillators that can be synchronized. Further, we show that the lack of long
range order is associated with the formation of topological defects in the
phase field similar to the two-dimensional XY model of ferromagnetism. Our
results shed new light on the synchronization of STO, where controlling the
mutual synchronization of several oscillators is considered crucial for
applications.Comment: Accepted for publication in Scientific Reports. Corrected typo in
Eq.(9) from previous versio
Restoration of rhythmicity in diffusively coupled dynamical networks
We acknowledge financial support from the National Natural Science Foundation of China (No. 11202082, No. 61203235, No. 11371367 and No. 11271290), the Fundamental Research Funds for the Central Universities of China under Grant No. 2014QT005, IRTG1740(DFG-FAPESP), and SERB-DST Fast Track scheme for young scientist under Grant No. ST/FTP/PS-119/2013, NSF CHE-0955555 and Grant No. 229171/2013-3 (CNPq).Peer reviewedPublisher PD
The Kuramoto model: A simple paradigm for synchronization phenomena
Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included
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