Critical exponents in coupled phase-oscillator models on small-world networks

Yoneda, Ryosuke; Harada, Kenji; Yamaguchi, Yoshiyuki Y.

doi:10.1103/physreve.102.062212

Cited by 4 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These parameters are varied to maximize the likelihood function. [21,22] The standard deviation for the estimate of the exponent was obtained from 1000 Monte Carlo samples. Unfortunately, a goodness-ofprobability p is not available for this method of fitting.…”

Section: Gaussian Process Fittingmentioning

confidence: 99%

Irrelevant Corrections at the Quantum Hall Transition

Slevin

Ohtsuki

2023

Physica Rapid Research Ltrs

View full text Add to dashboard Cite

The quantum Hall effect is one of the most extensively studied topological effects in solid‐state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous numerical finite size scaling studies have focused on the critical exponent ν for the correlation length. In such studies, it is important to take proper account of irrelevant corrections to scaling. Recently, Dresselhaus et al. proposed a new scaling ansatz, which they applied to the two terminal conductance of the Chalker–Coddington model. Herein, their proposal is applied to the previously reported data for the Lyapunov exponents of that model using both polynomial fitting and Gaussian process fitting.

show abstract

Section: Gaussian Process Fittingmentioning

confidence: 99%

Irrelevant Corrections at the Quantum Hall Transition

Slevin

Ohtsuki

2023

Physica Rapid Research Ltrs

View full text Add to dashboard Cite

show abstract

“…The assumptions on models here are that the system has mean-field, all-to-all homogeneous interactions and that the system lies in the nonsynchronized state, which is defied as the state with vanishing order parameters without an input in the limit of large system size. For the first assumption, it is worth remarking that the mean-field interaction is not extremely special, because the mean-field analysis is allowed in many other networks: small-world networks [31][32][33], scalefree networks [34], random networks [35], and oscillators on the one-dimensional lattice whose interaction strength decays algebraically with distance [36]. See also [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of phase dynamics from macroscopic observations based on linear and nonlinear response theories

Yamaguchi,

Terada

2024

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

We propose a method to reconstruct the phase dynamics in rhythmical interacting systems from macroscopic responses to weak inputs by developing linear and nonlinear response theories, which predict the responses in a given system. By solving an inverse problem, the method infers an unknown system: the natural frequency distribution, the coupling function, and the time delay which is inevitable in real systems. In contrast to previous methods, our method requires neither strong invasiveness nor microscopic observations. We demonstrate that the method reconstructs two phase systems from observed responses accurately. The qualitative methodological advantages demonstrated by our quantitative numerical examinations suggest its broad applicability in various fields, including brain systems, which are often observed through macroscopic signals such as electroencephalograms and functional magnetic response imaging.

show abstract

“…The essential assumptions on models are that the system has the mean-field, all-to-all homogeneous interactions and that the system lies in the nonsynchronized state. For the first assumption, it is worth remarking that the all-toall interaction may not be extremely special, because the criticality in the small-world network [24] belongs to the universality class of the all-to-all interaction [25,26]. The mean-field analysis employed here could be extended by assuming statistics in couplings [27,28].…”

mentioning

confidence: 99%

Reconstruction of Phase Dynamics from Macroscopic Observations Based on Linear and Nonlinear Response Theories

Yamaguchi¹,

Terada²

2023

Preprint

View full text Add to dashboard Cite

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phaseoscillators, we derive formulae which connect the responses with the system parameters including the time delay in interactions. We examine our method by applying it to two phase models, one of which describes a mean-field network of the Hodgkin-Huxley type neurons with a nonzero time delay. The method does not require much invasiveness nor microscopic observations, and these advantages highlight its broad applicability in various fields.

show abstract

Critical exponents in coupled phase-oscillator models on small-world networks

Cited by 4 publications

References 39 publications

Irrelevant Corrections at the Quantum Hall Transition

Irrelevant Corrections at the Quantum Hall Transition

Reconstruction of phase dynamics from macroscopic observations based on linear and nonlinear response theories

Reconstruction of Phase Dynamics from Macroscopic Observations Based on Linear and Nonlinear Response Theories

Contact Info

Product

Resources

About