Local network parameters can affect inter-network phase lags in central pattern generators

Weakly coupled phase oscillators and strongly coupled relaxation oscillators have different mechanisms for creating stable phase lags. Many oscillations in central pattern generators combine features of each type of coupling: local networks composed of strongly coupled relaxation oscillators are weakly coupled to similar local networks. This paper analyzes the phase lags produced by this combination of mechanisms and shows how the parameters of a local network, such as the decay time of inhibition, can affect the phase lags between the local networks. The analysis is motivated by the crayfish central pattern generator used for swimming, and uses techniques from geometrical singular perturbation theory.