A prominent feature of the solar cycle is the rise and fall of the number of sunspots on the surface with a timescale of approximately eleven years. The mathematical description of this behavior is complicated by the interruption of the cycle for 75 years starting around 1650. Similar previous intermissions of this kind are implied by the available data. We explore the possibility of modeling such temporal variations of the sunspot number with a deterministic dynamical system of relatively low order. The system we propose manifests on/off intermittency in which the cyclic variations of the solar activity switch off almost completely for extended periods. We also offer an explanation of the variation of the fluctuating part of the sunspot number over the cycle.