Electrodermal activity (EDA) is a measure of physical arousal, which is frequently measured during psychophysical tasks relevant for anxiety disorders. Recently, specific protocols and procedures have been devised in order to examine the neural mechanisms of fear conditioning and extinction. EDA reflects important responses associated with stimuli specifically administrated during these procedures. Although several previous studies have demonstrated the reproducibility of measures estimated from EDA, a mathematical framework associated with the stimulus-response experiments in question and, at the same time, including the underlying emotional state of the subject during fear conditioning and/or extinction experiments is not well studied. We here propose an ordinary differential equation model based on sudomotor nerve activity, and estimate the fear eliciting stimulus using a compressed sensing algorithm. Our results show that we are able to recover the underlying stimulus (visual cue or mild electrical shock). Moreover, relating the time-delay in the estimated stimulation to the visual cue during extinction period shows that fear level decreases as visual cues are presented without shock, suggesting that this feature might be used to estimate the fear state. These findings indicate that a mathematical model based on electrodermal responses might be critical in defining a low-dimensional representation of essential cognitive features in order to describe dynamic behavioral states.