Within the mammalian suprachiasmatic nucleus, multiple oscillators interact to coordinate circadian rhythms in behavior and physiology. We have developed a behavioral assay that disassociates central oscillators and allows rigorous study of their formal properties and interactions. Rodents held under 24h light:dark:light:dark (LDLD) cycles display "split" activity rhythms that reflect the reorganization of the central pacemaker into two oscillator groups cycling ~12h apart. After transfer to constant conditions, the two activity components rejoin through a series of transients lasting 2-7 days. Here we analyze fusion dynamics, characterize the underlying oscillator interactions, and assess two influencing factors: phase of transfer and lighting conditions upon transfer. Syrian hamsters were split under LDLD with dimly lit nights and then transferred to constant dim illumination or complete darkness during one of the two daily scotophases. Fusion was influenced by phase of transfer, suggesting that the oscillators split under LDLD exert an asymmetric influence over one another. Transfer to constant dim and dark conditions produced similar overall patterns of fusion, but nevertheless differed in the rejoined state of the system. The present results are discussed within a model wherein oscillators influence one another in a phase-dependent manner.