Noise-induced synchronization in small world networks of phase oscillators

Esfahani, Reihaneh Kouhi; Shahbazi, Farhad; Samani, Keivan Aghababaei

doi:10.1103/physreve.86.036204

Cited by 29 publications

(32 citation statements)

References 44 publications

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“…Such roles for noise bear similarity to the well-known stochastic resonance in physics, where noise can optimize the response of nonlinear systems to a weak external input [39]. Noise can also aid the synchronization of periodic [40,41] and chaotic [42] oscillators and networks of oscillators with various topologies [43,44]. Noise can also increase the regularity of activity in excitable systems [45].…”

Section: Introductionmentioning

confidence: 82%

“…Despite the geometry-and strength-sequence-preserving surrogate network (light blue) having the same weight-distance relationship and hub locations as the original brain network, and exhibiting similar coherence dynamics, noise does not enhance its syn-chronization, implying that more subtle topological features of the brain's wiring contribute to the effect such as possibly the brain's small-world topological structure (see Fig. S9 and Materials and Methods for details) [43]. These results reveal that the heterogeneity in the connectivity pattern, the hierarchy of the connectivity strengths of each node (Fig.…”

Section: Drivers Of Stochastic Synchronizationmentioning

confidence: 99%

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Stochastic synchronization of dynamics on the human connectome

Pang

Gollo

Roberts

2020

Preprint

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Synchronization is a collective mechanism by which oscillatory networks achieve their functions. Factors driving synchronization include the network's topological and dynamical properties. However, how these factors drive the emergence of synchronization in the presence of potentially disruptive external inputs like stochastic perturbations is not well understood, particularly for real-world systems such as the human brain. Here, we aim to systematically address this problem using a large-scale model of the human brain network (i.e., the human connectome). The results show that the model can produce complex synchronization patterns transitioning between incoherent and coherent states. When nodes in the network are coupled at some critical strength, a counterintuitive phenomenon emerges where the addition of noise increases the synchronization of global and local dynamics, with structural hub nodes benefiting the most. This stochastic synchronization effect is found to be driven by the intrinsic hierarchy of neural timescales of the brain and the heterogeneous complex topology of the connectome. Moreover, the effect coincides with clustering of node phases and strengthening of the functional connectivity of some of the connectome's subnetworks. Overall, the work provides broad theoretical insights into the emergence and mechanisms of stochastic synchronization, highlighting its putative contribution in achieving network integration underpinning brain function.

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Section: Introductionmentioning

confidence: 82%

Section: Drivers Of Stochastic Synchronizationmentioning

confidence: 99%

Stochastic synchronization of dynamics on the human connectome

Pang

Gollo

Roberts

2020

Preprint

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“…Besides the theoretical approaches described above, other aspects of the dynamics of the stochastic Kuramoto model were numerically addressed [283,[291][292][293][294][295]. In particular, Traxl et al [283] developed a numerical framework and systematically analyzed the influence of noise and coupling strength on the maximum degree of synchronization of several networks; including fully connected, random, modular and real topologies.…”

Section: Gaussian Approximationmentioning

confidence: 99%

“…If the generator properties, voltage magnitudes and line reactances are assumed to be the same, and all lines are lossless, i.e. ϕ ij = 0, one can reproduce the original second-order dynamics (292). Let us review first the derivation of the model via simplifying the swing equation.…”

Section: Power-gridsmentioning

confidence: 99%

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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“…This network showed SR in response to signals from central pattern generators, but noise-induced synchronization was not investigated. In a similar study, however, noise-induced synchronization was shown in a small-world network of identical phase oscillators (Esfahani et al 2012). Hence, SR and noise-induced synchronization can be induced in small-network models under certain conditions.…”

Section: Discussionmentioning

confidence: 77%

Random pulse induced synchronization and resonance in uncoupled non-identical neuron models

Nakamura

Tateno

2019

Cogn Neurodyn

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Random pulses contribute to stochastic resonance in neuron models, whereas common random pulses cause stochasticsynchronized excitation in uncoupled neuron models. We studied concurrent phenomena contributing to phase synchronization and stochastic resonance following induction by a weak common random pulse in uncoupled non-identical Hodgkin-Huxley type neuron models. The common random pulse was selected from a gamma distribution and the degree of synchronization depended on the corresponding shape parameter. Specifically, a low shape parameter of the weak random pulse induced well-synchronized spiking in uncoupled neuron models, whereas a high shape parameter of the weak random pulse or a weak periodic pulse caused low degrees of synchronization. These were improved by concurrent inputs of periodic and random pulses with high shape parameters. Finally, the output pulse was synchronized with the periodic pulse, and the common random pulse revealed periodic responses in the present neuron models.

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Noise-induced synchronization in small world networks of phase oscillators

Cited by 29 publications

References 44 publications

Stochastic synchronization of dynamics on the human connectome

Stochastic synchronization of dynamics on the human connectome

The Kuramoto model in complex networks

Random pulse induced synchronization and resonance in uncoupled non-identical neuron models

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