The effects of varying the timing of inputs on a neural oscillator

The gastric mill network of the stomatogastric ganglion of the crab Cancer borealis is comprised of a set of neurons that require modulatory input from outside the stomatogastric ganglion and input from the pyloric network of the animal in order to oscillate. Here we study how the frequency of the gastric mill network is determined when it receives rhythmic input from two different sources but where the timing of these inputs may differ. We find that over a certain range of the time difference one of the two rhythmic inputs plays no role what so ever in determining the network frequency, while in another range, both inputs work together to determine the frequency. The existence and stability of periodic solutions to model sets of equations are obtained analytically using geometric singular perturbation theory. The results are validated through numerical simulations. Comparisons to experiments are also presented.