Cells control the properties of the cytoplasm to ensure the proper functioning of biochemical processes. Recent studies showed that the density of the cytoplasm varies in both physiological and pathological states of cells undergoing growth, division, differentiation, apoptosis, senescence, and metabolic starvation. Little is known about how cellular processes cope with these cytoplasmic variations. Here we study how a cell cycle oscillator comprising cyclin -dependent kinase (CDK1) responds to cytoplasmic density changes by systematically diluting or concentrating a cycling Xenopus egg cytoplasm in cell-like microfluidic droplets. We found that the cell cycle maintains robust oscillations over a wide range of deviations from the endogenous density by as low as 0.2x to more than 1.22x. A further dilution or concentration from these values will arrest the system in a low or high steady-state of CDK1 activity, respectively. Interestingly, diluting a concentrated arrested cytoplasm recovers its oscillatory behavior but requires a significantly lower concentration than 1.22x. Thus, the cell cycle switches reversibly between oscillatory and stable steady states at distinct thresholds depending on the direction of density tuning, forming a hysteresis loop. We recapitulated these observations by a mathematical model. The model predicted that Wee1 and Cdc25 positive feedback do not contribute to the observed robustness, confirmed by experiments. Nevertheless, modulating these feedback strengths and cytoplasmic density changes the total number of cycles, revealing a new role of Wee1 and Cdc25 in controlling the cycle number of early embryonic extracts. Our system can be applied to study how cytoplasmic density affects other cellular processes.