Abstract

Biological and bio-inspired locomotion is usually described by recognizing periodic patterns, or gaits, in the movement of limbs or other body parts. But is the evolution of the system actually periodic? Or more properly, relative-periodic, since, presumably, each cycle will propel the animal (or robot) a little bit forward? The answer is often no, due, for instance, to inertia or elasticity. However, we might expect the behaviour to converge asymptotically to a relative-periodic one. In this talk we will introduce this issue considering, as a case study, a dynamic model of rectilinear crawling locomotion.

We study the existence of a global periodic attractor for the reduced dynamics of the model, corresponding to an asymptotically relative-periodic motion of the crawler. The main result is of Massera-type, namely we show that the existence of a bounded solution implies the existence of the global periodic attractor for the reduced dynamics. Additional conditions and a counterexample for the existence of a bounded solution (and therefore of the attractor) will be briefly discussed. We conclude surveying the issue for some related models.

Mathematical Physics and Dynamical Systems Seminar