Nature of synchronization transitions in random networks of coupled oscillators

Um, Jaegon; Hong, Hyunsuk; Park, Hyunggyu

doi:10.1103/physreve.89.012810

Cited by 21 publications

(31 citation statements)

References 25 publications

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“…2(c) confirm by the annealed MF th case with the bimoda transition with β = 1/ as seen in Fig. 2(d Adapted with permission from [70]. Copyrighted by the American Physical Society.…”

Section: Conclusion and Dsupporting

confidence: 59%

“…63 [69] The next is step is then verifying how the synchronization phase transition changes if the link-disorder is removed, while keeping the fluctuations in the frequency. More specifically, in this case, the connections between oscillators are kept constant over different realizations of the network dynamics (networks whose adjacency matrices are fixed over time or over different realizations are also referred as quenched networks [70,71]). At first, one could expect that the phase transition remains unchanged except from a shift in the coupling strength.…”

Section: Conclusion and Dmentioning

confidence: 99%

“…At first, one could expect that the phase transition remains unchanged except from a shift in the coupling strength. However, the scaling of r can significantly change whether the networks are quenched or annealed [70]. In order to illustrate this phenomenon, let us consider ER networks with uniform natural frequency distribution given by…”

Section: Conclusion and Dmentioning

confidence: 99%

See 2 more Smart Citations

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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“…2(c) confirm by the annealed MF th case with the bimoda transition with β = 1/ as seen in Fig. 2(d Adapted with permission from [70]. Copyrighted by the American Physical Society.…”

Section: Conclusion and Dsupporting

confidence: 59%

Section: Conclusion and Dmentioning

confidence: 99%

Section: Conclusion and Dmentioning

confidence: 99%

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The Kuramoto model in complex networks

et al. 2016

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“…In analogy with equilibrium critical phenomena, we expect the order parameter in the critical region to satisfy the FSS [14],…”

Section: Random Frequency Distributionmentioning

confidence: 99%

“…(3.7), we examine the local slopes of χ against | | in double logarithmic plots for very large N . The effective exponent γ eff is defined as 14) and the critical exponents are obtained from their asymptotic values as γ = lim →0 + γ eff ( ) and γ = lim →0 − γ eff ( ). Figure 4 shows the inverse of the effective exponent γ −1 eff as a function of .…”

Section: B Dynamic Fluctuationsmentioning

confidence: 99%

Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model

et al. 2015

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We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of the intrinsic frequencies of oscillators. For a population of size N , we study two ways of sampling the intrinsic frequencies according to the same given unimodal distribution g(ω). In the 'random' case, frequencies are generated independently in accordance with g(ω), which gives rise to oscillator number fluctuation within any given frequency interval. In the 'regular' case, the N frequencies are generated in a deterministic manner that minimizes the oscillator number fluctuations, leading to quasi-uniformly spaced frequencies in the population. We find that the two samplings yield substantially different finite-size properties with clearly distinct scaling exponents. Moreover, the hyperscaling relation between the order parameter and its fluctuations is valid in the regular case, but is violated in the random case. In this last case, a self-consistent mean-field theory that completely ignores dynamic fluctuations correctly predicts the FSS exponent of the order parameter but not its critical amplitude.

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Validity of annealed approximation in a high-dimensional system

Um,

Hong,

Park

2024

Sci Rep

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This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations governing dense-network systems converge to those of the complete-graph version in the thermodynamic limit, where link disorder fluctuations vanish entirely. Consequently, the annealed-network systems, where fluctuations are attenuated, also exhibit the same dynamic behavior in the thermodynamic limit. However, a significant discrepancy arises in the incoherent (disordered) phase wherein the finite-size behavior becomes critical in determining the steady-state pattern. To explicitly elucidate this discrepancy, we focus on identical oscillators subject to competitive attractive and repulsive couplings. In the incoherent phase of dense networks, we observe the manifestation of random irregular states. In contrast, the annealed approximation yields a symmetric (regular) incoherent state where two oppositely coherent clusters of oscillators coexist, accompanied by the vanishing order parameter. Our findings imply that the annealed approximation should be employed with caution even in dense-network systems, particularly in the disordered phase.

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Nature of synchronization transitions in random networks of coupled oscillators

Cited by 21 publications

References 25 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model

Validity of annealed approximation in a high-dimensional system

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