A salient dynamic property of social media is bursting behavior. In this paper, we study bursting behavior in terms of the temporal relation between a preceding baseline fluctuation and the successive burst response using a frequency time series of 3,000 keywords on Twitter. We found that there is a fluctuation threshold up to which the burst size increases as the fluctuation increases and that above the threshold, there appears a variety of burst sizes. We call this threshold the critical threshold. Investigating this threshold in relation to endogenous bursts and exogenous bursts based on peak ratio and burst size reveals that the bursts below this threshold are endogenously caused and above this threshold, exogenous bursts emerge. Analysis of the 3,000 keywords shows that all the nouns have both endogenous and exogenous origins of bursts and that each keyword has a critical threshold in the baseline fluctuation value to distinguish between the two. Having a threshold for an input value for activating the system implies that Twitter is an excitable medium. These findings are useful for characterizing how excitable a keyword is on Twitter and could be used, for example, to predict the response to particular information on social media.