Cell cycle progression is carefully coordinated with a cell's intra- and extracellular environment. While some pathways have been identified that communicate information from the environment to the cell cycle, a systematic understanding of how this information is dynamically processed is lacking. We address this by performing dynamic sensitivity analysis of three mathematical models of the cell cycle in Saccharomyces cerevisiae. We demonstrate that these models make broadly consistent qualitative predictions about cell cycle progression under dynamically changing conditions. For example, it is shown that the models predict anticorrelated changes in cell size and cell cycle duration under different environments independently of the growth rate. This prediction is validated by comparison to available literature data. Other consistent patterns emerge, such as widespread nonmonotonic changes in cell size down generations in response to parameter changes. We extend our analysis by investigating glucose signalling to the cell cycle, showing that known regulation of Cln3 translation and Cln1,2 transcription by glucose is sufficient to explain the experimentally observed changes in cell cycle dynamics at different glucose concentrations. Together, these results provide a framework for understanding the complex responses the cell cycle is capable of producing in response to dynamic environments.