Brains in sleep, anesthesia, and traumatic injury are characterized by significantly limited responsiveness to stimuli. Even during conscious wakefulness, responsiveness is highly dependent on on-going brain activity, specifically, of alpha oscillations (~10Hz). However, despite many empirical studies, the ways in which specific alpha oscillations induce a large or small response to stimuli have not been elucidated. We hypothesized that the variety of responses to sensory stimuli result from the interaction between state-specific and transient alpha oscillations and stimuli. To justify this hypothesis, we simulated various alpha oscillations in the human brain network, modulating network criticality (a balanced state between order and disorder), and investigated specific alpha oscillation properties (instantaneous amplitude, phase, and global synchronization) that induce a large or small response. We found that near a critical state, a large, complex response is induced when a stimulus is given to globally desynchronized and lowamplitude alpha oscillations, and we also found specific phases of alpha oscillation that barely respond to stimuli. These results imply the presence of temporal windows in the alpha cycle for a large or small response to external stimuli, which is consistent with the periodic perceptual binding at alpha frequency found in empirical studies.