Nonlinear dynamics and bifurcations of a planar undulating magnetic microswimmer

TL;DR

This paper investigates the complex nonlinear dynamics of a planar magnetic microswimmer, revealing new motion behaviors and bifurcations that can inform better design of magnetically-actuated nano-robots for biomedical use.

Contribution

It extends previous models by analyzing large-amplitude oscillations, uncovering multiple solutions, bifurcations, and optimal parameters for enhanced swimming performance.

Findings

Discovered faster backward swimming modes.

Analyzed bifurcations and symmetry breaking in the system.

Identified parameter regimes for maximum speed and efficiency.

Abstract

Swimming micro-organisms such as flagellated bacteria and sperm cells have fascinating locomotion capabilities. Inspired by their natural motion, there is an ongoing effort to develop artificial robotic nano-swimmers for potential in-body biomedical applications. A leading method for actuation of nano-swimmers is by applying a time-varying external magnetic field. Such systems have rich and nonlinear dynamics that calls for simple fundamental models. A previous work studied forward motion of a simple two-link model with passive elastic joint, assuming small-amplitude planar oscillations of the magnetic field about a constant direction. In this work, we found that there exists a faster, backward motion of the swimmer with very rich dynamics. By relaxing the small-amplitude assumption, we analyze the multiplicity of periodic solutions, as well as their bifurcations, symmetry breaking, and stability transitions. We have also found that the net displacement and/or mean swimming speed are maximized for optimal choices of various parameters. Asymptotic calculations are performed for the bifurcation condition and the swimmer's mean speed. The results may enable significantly improving the design aspects of magnetically-actuated robotic microswimmer.