Symmetry-breaking bifurcation: A possible mechanism for 2:1 frequency-locking in animal locomotion

The generation and control of animal locomotion is believed to involve central pattern generators — networks of neurons which are capable of producing oscillatory behavior. In the present work, the quadrupedal locomotor central pattern generator is modelled as four distinct but symmetrically coupled nonlinear oscillators. We show that the typical patterns for two such networks of oscillators include 2:1 frequency-locked oscillations. These patterns, which arise through symmetry-breaking Hopf bifurcation, correspond in part to observed patterns of 2:1 frequency-locking of limb movements during electrically elicited locomotion of decerebrate and spinal quadrupeds. We briefly describe how our theoretical predictions could be tested experimentally.