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In recent years, computational biologists have shown through simulation that small neural networks with fixed connectivity are capable of producing multiple output rhythms in response to transient inputs. It is believed that such networks may play a key role in certain biological behaviors such as dynamic gait control. In this paper, we present a novel method for designing continuous-time recurrent neural networks (CTRNNs) that contain multiple embedded limit cycles, and we show that it is possible to switch the networks between these embedded limit cycles with simple transient inputs. We also describe the design and testing of a fully integrated four-neuron CTRNN chip that is used to implement the neural network pattern generators. We provide two example multipattern generators and show that the measured waveforms from the chip agree well with numerical simulations.