Spatially extended systems supporting traveling waves exhibit a wide variety of novel dynamical behavior. This talk will focus on providing a theoretical explanation of patterns called chevrons, blinking states and repeated transients observed in binary fluid convection very close to the threshold of the primary instability. Direct numerical simulations in two-dimensional, laterally bounded containers reproduce the experiments quantitatively. The repeated transients are identified as a three-frequency state, and in many cases form the first nontrivial state of the system when the Rayleigh number is raised past its linear stability threshold. A dynamical systems explanation of this phenomenon is proposed.