A simple analytical model is proposed here that captures to a large extent the kinematic structure of rat exploratory behavior. Previous studies have shown that such behavior consists of regular excursions into the environment from a preferred place termed a home base. In the ®rst part of this study, we showed that with time and repeated exposure to the same large environment, there is a gradual increase in the length of excursions. Concurrently, the rat's velocity pattern changes in a complex yet structured way, which is correlated with the exposure (=familiarity) to places. In this part, we show that the complex pattern described there might be explained by an analytic model, in terms of a simple dynamical system, with few assumptions concerning motivation and learning. The model is studied both by analysis and simulation. The theoretical examination of the dynamics of excursion length suggests that excursion length increases as a linear function of two system parameters, one g...