The neuronal circuit that controls obsessive and compulsive behaviors involves a complex network of brain regions (some with known involvement in reward processing). Among these are cortical regions, the striatum and the thalamus (which compose the CSTC pathway), limbic areas such as the amygdala and the hippocampus, and well as dopamine pathways. Abnormal dynamic behavior in this brain network is a hallmark feature of patients with increased anxiety and motor activity, like the ones affected by OCD. There is currently no clear understanding of precisely what mechanisms generates these behaviors. We attempt to investigate a collection of connectivity hypotheses of OCD by means of a computational model of the brain circuitry that governs reward and motion execution. Mathematically, we use methods from ordinary differential equations and continuous time dynamical systems. We use classical analytical methods as well as computational approaches to study phenomena in the phase plane (e.g., behavior of the system's solutions when given certain initial conditions) and in the parameter space (e.g., sensitive dependence of initial conditions). We find that different obsessive-compulsive subtypes may correspond to different abnormalities in the network connectivity profiles. We suggest that it is combinations of parameters (connectivity strengths between regions), rather the than the value of any one parameter taken independently, that provides the best basis for predicting behavior, and for understanding the heterogeneity of the illness.