Which of the following circuit types is involved in the control of rhythmic activities such as
a) the sleep-wake cycle,
b) breathing,
c) and certain motor activities
(such as arm swinging when walking)?

The answer is Reverberating Circuit

Explanation:

reverberating circuits produces repetitive outputs. It involves signaling from one neuron to another in a linear sequence, one of the neurons sends a signal back to the initiating neuron. This is a back and forth signaling from one neuron to the neuron initiating the signal. It is involved in the control of activities that are rhythmic in nature such as breathing, the sleep-wake cycle, swinging of arms when walking.