The role of symmetry and dissipation in biolocomotion

TL;DR

This paper explores how symmetry and dissipation influence biolocomotion by analyzing a simplified 3D model that demonstrates the emergence of relative limit cycles, which could explain robust crawling and walking behaviors.

Contribution

It provides a detailed example of how symmetry reduction and dissipation can generate stable, periodic locomotion patterns in biological systems.

Findings

Relative limit cycles can emerge in dissipative systems with symmetry.

Symmetry reduction helps explain robustness in crawling and walking.

The model demonstrates how periodic perturbations lead to stable locomotion cycles.

Abstract

In this paper we illustrate the potential role which relative limit cycles may play in biolocomotion. We do this by describing, in great detail, an elementary example of reduction of a lightly dissipative system modeling crawling-type locomotion in 3D. The symmetry group SE(2) is the set of rigid transformations of the horizontal (ground) plane. Given a time-periodic perturbation, the system will admit a relative limit cycle whereupon each period is related to the previous by a fixed translation and rotation along the ground. This toy model identifies how symmetry reduction and dissipation can conspire to create robust behavior in crawling, and possibly walking, locomotion.