In this paper, we study the dynamics of coupled speed scaling systems, in which service rate is a function of system occupancy. We focus on both Processor Sharing (PS) and Shortest Remaining Processing Time (SRPT) as scheduling disciplines, and study their speed scaling dynamics under heavy load. Using a combination of Markov chain analysis and discrete-event simulation, we identify several important properties of speed scaling systems, which we call the autoscaling effect, the alpha effect, and the saturation effect. We also identify different overload regimes for PS and SRPT. In particular, SRPT exhibits a starvation effect that differs from the compensation effect of PS. These dynamics lead todifferent stability, fairness, and robustness properties for PS and SRPT under heavy load.