Synchronization in Coupled Phase Oscillators

Sakaguchi, Hidetsugu

doi:10.3938/jkps.53.1257

Cited by 8 publications

(7 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4 the eigenvector a(ρ) for a particular simulation run. The spiral center of the converged solution has been defined as the point of maximum a and the analytic expression (15) has been fitted to the data for k and a multiplicative constant. The good correspondence and ϕ-independence justifies the expression for a (15).…”

Section: B Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Frequency precision of two-dimensional lattices of coupled oscillators with spiral patterns

Allen

Cross

2013

Phys. Rev. E

View full text Add to dashboard Cite

Two-dimensional lattices of N synchronized oscillators with reactive coupling are considered as high-precision frequency sources in the case where a spiral pattern is formed. The improvement of the frequency precision is shown to be independent of N for large N , unlike the case of purely dissipative coupling where the improvement is proportional to N , but instead depends on just those oscillators in the core of the spiral that acts as the source region of the waves. Our conclusions are based on numerical simulations of up to N = 29 929 oscillators and analytic results for a continuum approximation to the lattice in an infinite system. We derive an expression for the dependence of the frequency precision on the reactive component of the coupling constant, depending on a single parameter given by fitting the frequency of the spiral waves to the numerical simulations.

show abstract

Section: B Resultsmentioning

confidence: 99%

“…For most of the paper we take σ = 0. Our coupling function is one commonly used [8,11,12,14,15] and has degree of reactive coupling γ . We choose units of time so that it takes the form…”

Section: Modelmentioning

confidence: 99%

Frequency precision of two-dimensional lattices of coupled oscillators with spiral patterns

Allen

Cross

2013

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…11 and ref. 12. Recently, synchronization in scalefree networks has been studied by several authors [13][14][15], and a model with two subpopulations corresponding to generators and loads was also studied in ref. 16.…”

Section: Introductionmentioning

confidence: 99%

Cascade Failure in a Phase Model of Power Grids

Sakaguchi

Matsuo

2012

J. Phys. Soc. Jpn.

Self Cite

View full text Add to dashboard Cite

We propose a phase model to study cascade failure in power grids composed of generators and loads. If the power demand is below a critical value, the model system of power grids maintains the standard frequency by feedback control. On the other hand, if the power demand exceeds the critical value, an electric failure occurs via step out (loss of synchronization) or voltage collapse. The two failures are incorporated as two removal rules of generator nodes and load nodes. We perform direct numerical simulation of the phase model on a scale-free network and compare the results with a mean-field approximation.Comment: 7 pages, 2 figure

show abstract

“…One of the recent topics is the synchronization in various types of networks [3][4][5]. The network structure itself is intensively investigated in physics.…”

Section: Introductionmentioning

confidence: 99%

“…The synchronization in coupled oscillators has intensively been studied [1,2]. One of the recent topics is the synchronization in various types of networks [3][4][5]. The network structure itself is intensively investigated in physics.…”

Section: Introductionmentioning

confidence: 99%

Phase Model with Feedback Control for Power Grids

Matsuo

Sakaguchi

2013

J. Phys. Soc. Jpn.

Self Cite

View full text Add to dashboard Cite

A phase model with feedback control is studied as a dynamical model of power grids. As an example, we study a model network corresponding to the power grid in the Kyushu region. The standard frequency is maintained by the mutual synchronization and the feedback control. Electric failures are induced by an overload. We propose a local feedback method in which the strength of feedback control is proportional to the magnitude of generators. We find that the electric failures do not occur until the utilization ratio is close to 1 under this feedback control. We also find that the temporal response for the time-varying input power is suppressed under this feedback control. We explain the mechanisms using the corresponding global feedback method.

show abstract

Synchronization in Coupled Phase Oscillators

Cited by 8 publications

References 6 publications

Frequency precision of two-dimensional lattices of coupled oscillators with spiral patterns

Frequency precision of two-dimensional lattices of coupled oscillators with spiral patterns

Cascade Failure in a Phase Model of Power Grids

Phase Model with Feedback Control for Power Grids

Contact Info

Product

Resources

About