The attentional blink (AB) effect is the reduced ability of subjects to report a second target stimuli (T2) amonga rapidly presented series of non-target stimuli, when it appears within a time window of about 200-500 msafter a first target (T1). We present a simple dynamical systems model explaining the AB as resulting fromthe temporal response dynamics of a stochastic, linear system with threshold, whose output represents theamount of attentional resources allocated to the incoming sensory stimuli. The model postulates that theavailable attention capacity is limited by activity of the default mode network (DMN), a correlated set ofbrain regions related to task irrelevant processing which is known to exhibit reduced activation followingmental training such as mindfulness meditation. The model provides a parsimonious account relating keyfindings from the AB, DMN and meditation research literature, and suggests some new testable predictions.