Predicting the nonlinear shift of stable equilibria in interlimb rhythmic coordination

A major prediction of the elementary coordination dynamics of two contralateral limb segments in 1 : 1 frequency locking was tested. A shift in stable steady-state relative phase φ from 0 and π radians is induced by a difference Δω in the uncoupled frequencies of the segments. The elementary coordination dynamics, an order parameter equation in φ, predicts that equilibrium shift will be a third-order polynomial function of Δω with a cubic coefficient that is (a) positive when the control parameter is constant, and (b) negative when the control parameter decreases with Δω. The prediction was confirmed in an experiment that manipulated Δω through differential loadings and the control parameter through coupled frequency. Implications for the dynamical modelling of coordination were discussed.