The antennal lobe plays a central role for odor processing in insects, as demonstrated by electrophysiological and imaging experiments. Here we analyze the detailed temporal evolution of glomerular activity patterns in the antennal lobe of honeybees. We represent these spatiotemporal patterns as trajectories in a multidimensional space, where each dimension accounts for the activity of one glomerulus. Our data show that the trajectories reach odor-specific steady states (attractors) that correspond to stable activity patterns at about 1 second after stimulus onset. As revealed by a detailed mathematical investigation, the trajectories are characterized by different phases: response onset, steady-state plateau, response offset, and periods of spontaneous activity. An analysis based on support-vector machines quantifies the odor specificity of the attractors and the optimal time needed for odor discrimination. The results support the hypothesis of a spatial olfactory code in the antennal lobe and suggest a perceptron-like readout mechanism that is biologically implemented in a downstream network, such as the mushroom body.