Which preposition to use with periodicity

of Occurrences 6%

Just as the sex glands influence the body and mind profoundly with a certain cyclic periodicity of activity and inactivity (rut, heat, menstrual period and so on), which has been demonstrated to have a very close functional relationship with the pituitary, so sleep and hibernation will bear interpretation as products of a temporary dormancy of the same gland.

in Occurrences 3%

1872 May 9 On a Supposed Periodicity in the R. Soc.

Which preposition to use with  periodicity