Flow control mechanisms are essential for the efficient and stable operation of store-and-forward networks. New transport protocols, such as VMTP and NETBLT, intend to use rate-based flow control. We present a model in which a network with connections subject to rate-based flow control is considered as a dynamical system, i.e., a set of coupled differential equations. We consider two scenarios: (1) a single connection over a long delay path involving a bottleneck; and (2) two connections with different roundtrip delays that share a common bottleneck. For a recently proposed control scheme, we obtain closed-form solutions for the dynamical model in both transient and steady state regimes, and evaluate appropriate performance measures. We compare our results with those obtained by others using experimental and simulation approaches.