  Interactions in nature can be described by their coupling strength, direction
of coupling and coupling function. The coupling strength and directionality are
relatively well understood and studied, at least for two interacting systems,
however there can be a complexity in the interactions uniquely dependent on the
coupling functions. Such a special case is studied here { synchronization
transition occurs only due to the time-variability of the coupling functions,
while the net coupling strength is constant throughout the observation time. To
motivate the investigation, an example is used to present an analysis of
cross-frequency coupling functions between delta and alpha brainwaves extracted
from the electroencephalography (EEG) recording of a healthy human subject in a
freerunning resting state. The results indicate that time-varying coupling
functions are a reality for biological interactions. A model of phase
oscillators is used to demonstrate and detect the synchronization transition
caused by the varying coupling functions, during an invariant coupling
strength. The ability to detect this phenomenon is discussed with the method of
dynamical Bayesian inference, which was able to infer the time-varying coupling
functions. The form of the coupling function acts as an additional dimension
for the interactions and it should be taken into account when detecting
biological or other interactions from data.
