Phase synchronization and noise-induced resonance in systems of coupled oscillators

Hong, Hyunsuk; My, Choi

doi:10.1103/physreve.62.6462

Cited by 28 publications

(13 citation statements)

References 54 publications

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“…The critical coupling strength increases monotonically with the increase of D [312]. Moreover, via analyzing the power spectrum of the phase velocity, in contrast with synchronization suppressed by noise, the response of the phase velocity to the external driving is enhanced by a certain amount of noise [312]. Meanwhile, two related results were obtained: a consistent two-term Smoluchowski approximate equation in the limit of small inertia and the amplitude equation for an O(2)-symmetric Takens-Bogdanov bifurcation at the tricritical point of a standard Kuramoto model using the Chapman-Enskog method [311].…”

Section: Mean-field Theory With Noisementioning

confidence: 97%

“…For D = 0, by analyzing the stationary state of Eq. 313, the self-consistent equation is obtained [312] …”

Section: Mean-field Theory With Noisementioning

confidence: 99%

“…The hysteresis is reduced with the presence of noise. The critical coupling strength increases monotonically with the increase of D [312]. Moreover, via analyzing the power spectrum of the phase velocity, in contrast with synchronization suppressed by noise, the response of the phase velocity to the external driving is enhanced by a certain amount of noise [312].…”

Section: Mean-field Theory With Noisementioning

confidence: 99%

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The Kuramoto model in complex networks

et al. 2016

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Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

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Section: Mean-field Theory With Noisementioning

confidence: 97%

“…For D = 0, by analyzing the stationary state of Eq. 313, the self-consistent equation is obtained [312] …”

Section: Mean-field Theory With Noisementioning

confidence: 99%

Section: Mean-field Theory With Noisementioning

confidence: 99%

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The Kuramoto model in complex networks

et al. 2016

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“…Moreover, neural firings and network learning depend mutually on each other, thus giving rise to codependent dynamics. Such coupled nonlinear dynamical systems may exhibit rich complex behaviors such as stochastic and coherence resonances (Gang et al, 1993;Pikovsky and Kurths, 1997;Lee et al, 1998;Hong and Choi, 2000) as well as synchronization, found to be enhanced by the small-world wiring structure (Hong et al, 2002;Wang and Chen, 2002). Such synchronous neural activity also exerts effects on the network development by perturbing or even reversing the firing order in a synapse (Cho and Choi, 2007).…”

Section: Network Development Modelsmentioning

confidence: 97%

Brain networks: Graph theoretical analysis and development models

Cho

Choi

2010

Int J Imaging Syst Tech

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A trendy method to understand the brain is to make a map representing the structural network of the brain, also known as the connectome, on the scale of a brain region. Indeed analysis based on graph theory provides quantitative insights into general topological principles of brain network organization. In particular, it is disclosed that typical brain networks share the topological properties, such as small-world and scale-free, with many other complex networks encountered in nature. Such topological properties are regarded as characteristics of the optimal neural connectivity to implement efficient computation and communication; brains with disease or abnormality show distinguishable deviations in the graph theoretical analysis. Considering that conventional models in graph theory are, however, not adequate for direct application to the neural system, we also discuss a model for explaining how the neural connectivity is organized.

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“…This second order phase oscillator model is a generalization of the well-known integrate and fire neuron to the case of medium to strong coupling, or equivalently, weak damping [42]. This type of second order oscillator model has been studied numerically in the context of phase synchronization [26], phase-frequency synchronization [43,44], and the emergence of spontaneous oscillations due to time delay and inertia [45,46].…”

Section: The Modelmentioning

confidence: 99%

Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

Majtanik¹,

Dolan²,

Tass

2006

J Biol Phys

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Effective desynchronization can be exploited as a tool for probing the functional significance of synchronized neural activity underlying perceptual and cognitive processes or as a mild treatment for neurological disorders like Parkinson's disease. In this article we show that pulse-based desynchronization techniques, originally developed for networks of globally coupled oscillators (Kuramoto model), can be adapted to networks of coupled neurons with dendritic dynamics. Compared to the Kuramoto model, the dendritic dynamics significantly alters the response of the neuron to the stimulation. Under medium stimulation amplitude a bistability of the response of a single neuron is observed. When stimulated at some initial phases, the neuron displays only modulations of its firing, whereas at other initial phases it stops oscillating entirely. Significant alterations in the duration of stimulation-induced transients are also observed. These transients endure after the end of the stimulation and cause maximal desynchronization to occur not during the stimulation, but with some delay after the stimulation has been turned off. To account for this delayed desynchronization effect, we have designed a new calibration procedure for finding the stimulation parameters that result in optimal desynchronization. We have also developed a new desynchronization technique by low frequency entrainment. The stimulation techniques originally developed for the Kuramoto model, when using the new calibration procedure, can also be applied to networks with dendritic dynamics. However, the mechanism by which desynchronization is achieved is substantially different than for the network of Kuramoto oscillators. In particular, the addition of dendritic dynamics significantly changes the timing of the stimulation required to obtain desynchronization. We propose desynchronization stimulation for experimental analysis of synchronized neural processes and for the therapy of movement disorders.

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Phase synchronization and noise-induced resonance in systems of coupled oscillators

Cited by 28 publications

References 54 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Brain networks: Graph theoretical analysis and development models

Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

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