Multibranch Entrainment and Slow Evolution among Branches in Coupled Oscillators

Aonishi, Toru; Okada, Masato

doi:10.1103/physrevlett.88.024102

Cited by 14 publications

(3 citation statements)

References 12 publications

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“…Detailed theoretical understanding of stability of the asynchronous states constructed via the self-consistency approach in this paper, is still missing. Finally, noise regularizes the multiplicity of the micro-states and turns neutral stabil-ity into an asymptotic one [40,20]; these effects will be discussed in details elsewhere [22].…”

Section: Resultsmentioning

confidence: 99%

The Kuramoto model of coupled oscillators with a bi-harmonic coupling function

Komarov

Pikovsky

2014

Physica D: Nonlinear Phenomena

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We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent equations describing uniformly rotating complex order parameters, both for single-branch (one possible state of locked oscillators) and multi-branch (two possible values of locked phases) entrainment. We show that synchronous states coexist with the neutrally linearly stable asynchronous regime. The latter has a finite life time for finite ensembles, this time grows with the ensemble size as a power law.

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Section: Resultsmentioning

confidence: 99%

The Kuramoto model of coupled oscillators with a bi-harmonic coupling function

Komarov

Pikovsky

2014

Physica D: Nonlinear Phenomena

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“…It is difficult to specify such a transfer function concretely, but it is possible to introduce one formally. As a premise that this transfer function holds, we assume that the microscopic memory effect can be neglected in the steady state [64].…”

Section: Outline Of Derivation Of Mes For the Whole Hybrid Systemmentioning

confidence: 99%

L0 regularization-based compressed sensing with quantum–classical hybrid approach

Aonishi

Mimura

Okada

et al. 2022

Quantum Sci. Technol.

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L0-regularization-based compressed sensing (L0-RBCS) has the potential to outperform L1-regularization-based compressed sensing (L1-RBCS), but the optimization in L0-RBCS is difficult because it is a combinatorial optimization problem. To perform optimization in L0-RBCS, we propose a quantum-classical hybrid system consisting of a quantum machine and a classical digital processor. The coherent Ising machine (CIM) is a suitable quantum machine for this system because this optimization problem can only be solved with a densely connected network. To evaluate the performance of the CIM-classical hybrid system theoretically, a truncated Wigner stochastic differential equation (W-SDE) is introduced as a model for the network of degenerate optical parametric oscillators, and macroscopic equations are derived by applying statistical mechanics to the W-SDE. We show that the system performance in principle approaches the theoretical limit of compressed sensing and this hybrid system may exceed the estimation accuracy of L1-RBCS in actual situations, such as in magnetic resonance imaging data analysis.

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“…For instance, the choice H ij (θ) = sin(θ) yields the classical Kuramoto model [10], while the presence of additional modes can give rise to multibranch entrainment, a.k.a. cluster synchronization [30][31][32][33][34][35][36][37]. Here, we focus our attention on systems with coupling frustration, as indicated by one or more non-zero values of the quantity…”

Section: Introductionmentioning

confidence: 99%

Erosion of synchronization: Coupling heterogeneity and network structure

Skardal

Taylor

Sun

et al. 2016

Physica D: Nonlinear Phenomena

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We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength. Here, we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization. Our analytical results are given in terms of basic quantities related to the network structure and coupling frustration. In addition to fully heterogeneous coupling, where each individual interaction is allowed to be distinct, we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions, respectively. We demonstrate the validity of our theory with numerical simulations of multiple network models, and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization. Finally, we consider some special network structures with well-known spectral properties, which allows us to derive further analytical results.

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Multibranch Entrainment and Slow Evolution among Branches in Coupled Oscillators

Cited by 14 publications

References 12 publications

The Kuramoto model of coupled oscillators with a bi-harmonic coupling function

The Kuramoto model of coupled oscillators with a bi-harmonic coupling function

L0 regularization-based compressed sensing with quantum–classical hybrid approach

Erosion of synchronization: Coupling heterogeneity and network structure

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