Chaos Lab

Continuous flow · dim ∞

Kuramoto coupled oscillators

N globally coupled phase oscillators with frequencies ω_i drawn from some distribution. Above a critical coupling K_c the population synchronises. Exhibits chimera states under specific topologies.

N = 64 Kuramoto oscillators at K = 1.6 near synchronisation threshold; orange arrow = mean-field order parameter.

Equations

dθ_i/dt = ω_i + (K/N) Σ_j sin(θ_j − θ_i)

At a glance

ParametersK, ω_i, N
Chaotic forvaries; chimeras in non-locally coupled rings
HistoryKuramoto (1975); chimera states by Kuramoto and Battogtokh (2002).

See also

Quick quiz

Test yourself on kuramoto

8 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.Above the critical coupling K_c in Kuramoto's model:

  2. Q2.Chimera states are:

  3. Q3.The Kuramoto order parameter r is:

  4. Q4.Yoshiki Kuramoto introduced the model in:

  5. Q5.The Kuramoto-Sakaguchi extension adds:

  6. Q6.Application of Kuramoto's model:

  7. Q7.Mean-field assumption in Kuramoto:

  8. Q8.Chimera states require which topology?

0 of 8 answered