Research into the neural correlates of consciousness has found that the vividness and complexity of conscious experience is related to the structure of brain dynamics, and that alterations to consciousness track changes in temporal evolution of brain states. Despite inducing externally similar states, propofol and ketamine produce different subjective states of consciousness. Here we explore the different effects of these two anaesthetics on the structure of dynamical attractors reconstructed from brain activity recorded electrophysiologically from cerebral cortex of a non-human primate. We used two different methods of attractor reconstruction. The first embeds the recordings in a continuous high-dimensional manifold on which we use topological data analysis to infer the presence (or absence) of higher-order dynamics. The second reconstruction, an ordinal partition network embedding, allows us to create a discrete state-transition network approximation of a continuous attractor, which is amenable to information-theoretic analysis and contains rich information about state-transition dynamics. We find significant differences between the awake, ketamine, and propofol conditions. Propofol significantly decreased the expression of higher-order structure in brain dynamics, while ketamine had the opposite effect, promoting an increase in complex dynamic features. Overall we found that ketamine produced dynamics similar to normal waking consciousness while propofol did not, and the significance of these findings is discussed. different drugs with a specific focus on how different dynamics might relate to conscious awareness [55,63]. In this paper, we take such a comparative approach to explore the differences between the effects of propofol and ketamine on multi-scale brain dynamics with an eye specifically to how these dynamics might explain the differences in consciousness induced by both drugs. Here we characterize brain dynamics by adapting two complementary models capturing the evolution of whole-brain states through time: the first plots a trajectory through a high-dimensional configuration space, while the other discretizes transitions into a Markovian state-transition network.While ketamine and propofol are both classified broadly as anesthetics, and both obliterate consciousness at high doses, it is useful to compare their different pharmacologies and the differences between the states they induce at low-to-moderate doses. By binding to GABA A receptors, propofol triggers widespread inhibition of neuronal activity and even at low doses, induces states of amnesia, sedation, atonia, and at higher doses, full anesthesia [29,23]. In contrast, ketamine acts primarily as an antagonist of glutamaterigic NMDA receptors [29,66], causing widespread, light central nervous system stimulation and a state typically referred to as "dissociative anesthesia" [16,33]. Unlike propofol, which simply ablates consciousness, an otherwise unresponsive patient anesthetized with ketamine often continues to have complex, conscious experi...