Author Summary Responsiveness of the brain varies depending on the brain states (wakefulness, sleep, anesthesia, and traumatic injuries) and even during wakefulness, resulting in various responses to the same stimulus. What makes those different responses across brain states and even across time windows in conscious state? What is an effective way to obtain the largest response to external stimulus? To answer those questions, we simulated various alpha oscillations (∼10 Hz) in a large-scale brain network and found state-specific alpha oscillation properties that show large or small responsiveness. Notably, the results suggest the presence of temporal windows in alpha cycle that inhibit external information integration and emphasize considering the large/small responsiveness conditions for effective brain stimulation. Abstract Brains in unconsciousness are characterized by significantly limited responsiveness to stimuli. Even during conscious wakefulness, responsiveness is highly dependent on ongoing brain activity, specifically, of alpha oscillations (∼10 Hz). We hypothesized that the variety of brain responses to external 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 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. As a result, we found that the alpha oscillations near a critical state show a more complex and long-lasting response, which is more prominent when stimuli are given to globally desynchronized and low-amplitude oscillations. We also found specific phases of alpha oscillation that barely respond to stimuli, which implies the presence of temporal windows in the alpha cycle for a large or small response. The results explain why brain responses are so variable across conscious and unconscious states and across time windows even during conscious wakefulness, and emphasize the importance of considering ongoing alpha oscillations for effective brain stimulation.