Robust entrainment to natural oscillations of asymmetric systems arising from animal locomotion

We consider a class of linear flexible mechanical systems arising from the dynamics of animal locomotion. A distinctive property of such systems is that the stiffness matrix is asymmetric. Extending the standard notion to this class, we define the natural oscillation as a free response under the damping compensation to achieve marginal stability. As a benchmark, a link chain system in a fluid environment is considered, and its natural oscillation is shown to exhibit travelling waves appropriate for undulatory swimming. Moreover, we propose nonlinear feedback controllers, inspired by neuronal dynamics, to achieve entrainment to the natural oscillation.