2007
DOI: 10.1007/978-3-540-71269-5
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Synchronization in Oscillatory Networks

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Cited by 400 publications
(292 citation statements)
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“…Among such phase oscillators networks, the often encountered and most thoroughly studied case is that of anti-symmetric coupling without higher-order harmonics, that is, the oscillator network (1) with sinusoidal coupling. Moreover, the coupled oscillator model (1) serves as the prototypical example for synchronization in complex networks (Strogatz, 2001;Boccaletti et al, 2006;Osipov et al, 2007;Suykens and Osipov, 2008;Arenas et al, 2008), and its linearization is the well-known consensus protocol studied in networked control, see the surveys and monographs (Olfati-Saber et al, 2007;Ren et al, 2007;Bullo et al, 2009;Garin and Schenato, 2010;Mesbahi and Egerstedt, 2010). Indeed, numerous control scientists explored the coupled oscillator model (1) as a nonlinear generalization of the consensus protocol (Jadbabaie et al, 2004;Moreau, 2005;Scardovi et al, 2007;Olfati-Saber, 2006;Lin et al, 2007;Chopra and Spong, 2009;Sarlette and Sepulchre, 2009;Sepulchre, 2011).…”
Section: Canonical Model and Prototypical Examplementioning
confidence: 99%
See 1 more Smart Citation
“…Among such phase oscillators networks, the often encountered and most thoroughly studied case is that of anti-symmetric coupling without higher-order harmonics, that is, the oscillator network (1) with sinusoidal coupling. Moreover, the coupled oscillator model (1) serves as the prototypical example for synchronization in complex networks (Strogatz, 2001;Boccaletti et al, 2006;Osipov et al, 2007;Suykens and Osipov, 2008;Arenas et al, 2008), and its linearization is the well-known consensus protocol studied in networked control, see the surveys and monographs (Olfati-Saber et al, 2007;Ren et al, 2007;Bullo et al, 2009;Garin and Schenato, 2010;Mesbahi and Egerstedt, 2010). Indeed, numerous control scientists explored the coupled oscillator model (1) as a nonlinear generalization of the consensus protocol (Jadbabaie et al, 2004;Moreau, 2005;Scardovi et al, 2007;Olfati-Saber, 2006;Lin et al, 2007;Chopra and Spong, 2009;Sarlette and Sepulchre, 2009;Sepulchre, 2011).…”
Section: Canonical Model and Prototypical Examplementioning
confidence: 99%
“…The network science, nonlinear dynamics, and physics communities coined the term complex for such non-trivial topologies to distinguish them from longrange (complete) and short-range (lattice-type) interaction topologies. The interest in such complex oscillator networks has been sparked by the seminal article (Jadbabaie et al, 2004) and the widespread scientific attention given to complex network studies (Strogatz, 2001;Boccaletti et al, 2006;Osipov et al, 2007;Arenas et al, 2008;Suykens and Osipov, 2008;Dorogovtsev et al, 2008), and consensus and its applications (Olfati-Saber et al, 2007;Ren et al, 2007;Bullo et al, 2009;Garin and Schenato, 2010;Mesbahi and Egerstedt, 2010).…”
Section: Synchronization In Sparse Networkmentioning
confidence: 99%
“…We may ask how such different systems show similar dynamical responses (e.g., generation and spatiotemporal distribution of defects) when they undergo an instability towards a "new state." Precedents on synchronization are found in the pioneering work by Winfree [1] and Kuramoto [2] and in the research on collective behavior in life sciences like neurology [3], ecology [4], and networks [5][6][7][8][9][10]. However, joint experimental [11][12][13][14][15] and theoretical [16][17][18] efforts have been scarce, and more research must be devoted to the understanding of synchronization processes in complex systems from the networks approach.…”
Section: Introductionmentioning
confidence: 99%
“…Sensory processing in animals is shaped by the ubiquitous presence of background noise, requiring the separation of signal from noise (Dusenbery 1992). As a further step, the concept of stochastic resonance deals with the use of noise to increase the sensitivity of sensory systems (Osipov et al 2007). For example, electrosensitive paddlefishes use stochastic resonance for homing in on Daphnia prey (Russell et al 1999).…”
Section: Future Challenges Taking the Lab To The Fieldmentioning
confidence: 99%