Synchronization:a universal concept in nonlinear science

By Peter V. E. McClintock. 2003

1,013 citations recorded by the source corpus.

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Citations in the corpus

Central pattern generators for locomotion control in animals and robots: A review (2008, background): “…approaches have been developed for analyzing systems of coupled oscillators (Ermentrout & Kopell, 1991; Slotine & Li, 1991; Kopell, 1995; Pikovsky et al., 2001; Golubitsky & Stewart, 2002; Wang & Slotine, 2005; Pham & Slotine, 2007), but many of these tools are not yet sufficient to…”
The concept of entrainment and its significance for ethnomusicology (2004, methodology): “It also demonstrates that in music we are rarely, if at all, dealing with strictly periodic oscillations, but exact periodicity has been shown to be not a prerequisite for entrainment (e.g. Pikovsky et al. 2001).”
Low dimensional behavior of large systems of globally coupled oscillators. (2008, background): “Understanding the generic behavior of systems consisting of large numbers of coupled oscillators is of great interest because such systems occur in a wide variety of significant applications[1].”
Dynamic hebbian learning in adaptive frequency oscillators (2006, background): “ṙ = (μ − r(2))r + F cos φ (3) φ̇ = ω − r F sin φ (4) It is well known that when the oscillator has its intrinsic frequency ω close to one frequency component of the periodic input, it will phase-lock (this phenomena is also called entrainment) [19].”
Partial synchronization: from symmetry towards stability (2002, background): “A large number of examples of synchronization in nature can be found in [8], and references therein.”
Chaos synchronization of a chaotic system via nonlinear control (2005, background): “For the state of the art, see two books [2,3].”
Nonlinear multivariate analysis of neurophysiological signals. (2005, methodology): “It is well known at present that the phases of two coupled nonlinear (noisy or chaotic) oscillators may synchronize even if their amplitudes remain uncorrelated, a state referred to as PS (Pikovsky et al., 2001).”
Connection Graph Stability Method for Synchronized Coupled Chaotic Systems (2004, methodology): “In a companion paper (“Blinking model and synchronization in small-world networks with a time-varying coupling,” see this issue), this method is extended to the blinking model of small-world networks where, in addition to the fixed 2K-nearest neighbor interactions, all the remaining links are…”
Stochastic resonance and sensory information processing: a tutorial and review of application. (2004, methodology): “…SR enhances phase locking and coherence and promotes synchronization in neuronal systems, according to simulation studies and experiments (Neiman et al., 1998, 1999; Bahar et al., 2002; Bahar and Moss, 2003a; Balazsi et al., 2001; Neiman and Russell, 2002; Tass et al., 2003; Pikovsky et al., 2001).”
Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators (2002, background): “Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into two domains, one composed of mutually synchronized oscillators with unique frequency and the other composed of desynchronized oscillators with distributed…”
Injection locking of VCSELs (2003, background): “Similar Arnold tongue structures can be found in many coupled oscillator systems to describe the conditions when the coupled oscillators are synchronized [10].”
Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing (2006, methodology): “A more technical description is given by Strogatz [1994], Schuster [1989] and Pikovsky et al. [2001]; Tziperman et al.”
Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop (2005, background): “The recovery of the message is based on the synchronization phenomenon [3], [4] by which a receiver, quite similar to the transmitter, is able to reproduce the chaotic part of the transmitted signal.”