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 non-linear 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.