Any process that modulates the frequency, rate or extent of contraction of the actomyosin ring involved in cytokinesis that takes place as part of a cell cycle.
Synonyms:
exact_synonym:
regulation of actomyosin contractile ring constriction; regulation of contractile ring contraction involved in cell cycle cytokinesis
related_synonym:
regulation of contractile ring contraction involved in cytokinesis during cell cycle