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The dynamical mechanism underlying the processes of anesthesia-induced loss of consciousness and recovery is key to gaining insights into the working of the nervous system. Previous experiments revealed an asymmetry between neural signals during the anesthesia and recovery processes. Here we obtain experimental evidence for the hysteresis loop and articulate the dynamical mechanism based on percolation on multilayer complex networks with self-similarity. Model analysis reveals that, during anesthesia, the network is able to maintain its neural pathways despite the loss of a substantial fraction of the edges. A predictive and potentially testable result is that, in the forward process of anesthesia, the average shortest path and the clustering coefficient of the neural network are markedly smaller than those associated with the recovery process. This suggests that the network strives to maintain certain neurological functions by adapting to a relatively more compact structure in response to anesthesia.