Synchronization, explained.
Synchronization is coordination of dynamical rhythms through interaction, often including frequency locking despite different uncoupled frequencies.
Why it happens
Two phase oscillators have natural angular speeds one and 1.4 with symmetric positive Kuramoto coupling K. Integration uses steps of 0.05. Stable locking requires K greater than 0.2 and can retain a nonzero phase gap.
Synchronization is coordination of dynamical rhythms through interaction, often including frequency locking despite different uncoupled frequencies.
Read the result
A stable phase gap indicates frequency locking, not necessarily equal phase. Plot wraps at plus or minus pi are coordinate changes.
A worked example
Couple two initially different rhythms
Advance the uncoupled oscillators to see the phase difference drift under speeds one and one point four.
Raise coupling above zero point two and allow several model time units for a stable gap to emerge.
Compare the bounded gap with the uncoupled drift while retaining the finite integration and two-node assumptions.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Two phase oscillators have natural angular speeds one and 1.4 with symmetric positive Kuramoto coupling K. Integration uses steps of 0.05. Stable locking requires K greater than 0.2 and can retain a nonzero phase gap.
Where this idea is useful
A practical use
When two rhythms align, ask what interaction supplies coupling and whether frequency matching also implies identical phase.
A common misconception
“Synchronisation requires both hands to point in exactly the same direction.”
Frequency-locked oscillators can maintain a stable nonzero phase difference when their natural frequencies differ.
What this explanation leaves out
- A two-node positively coupled phase model omits amplitude, noise and network structure. A wrapped plotting jump is not a physical discontinuity.
Why does the phase plot sometimes jump vertically?
Angles are wrapped to the interval from minus pi to pi; crossing that reporting boundary does not make the physical oscillator jump.
Are two processes sharing a frequency, a phase, or only an occasional coincidence?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.