Rectifying electrical synapses are commonplace, but surprisingly little is known about how rectification alters the dynamics of neuronal networks. In this study, we use computational models to investigate how rectifying electrical synapses change the behavior of a small neuronal network that exhibits complex rhythmic output patterns. We begin with an electrically coupled circuit of three oscillatory neurons with different starting frequencies, and subsequently add two additional neurons and inhibitory chemical synapses. The five-cell model represents a pattern-generating neuronal network with two simultaneous rhythms competing for the recruitment of a hub neuron. We compare four different configurations of rectifying synapse placement and polarity, and we investigate how rectification changes the functional output of this network. Rectification can have a striking effect on the network's sensitivity to alterations of the strengths of the chemical synapses in the network. For some configurations, the rectification makes the circuit dynamics remarkably robust against changes in synaptic strength compared with the nonrectifying case. Based on our findings, we predict that modulation of rectifying electrical synapses could have functional consequences for the neuronal circuits that express them.