A transport equation model and diffusion approximation for the walk of whirligig beetles

Abstract

The circular walk of whirligig beetles, in the absence of swarming behaviour, is described by a coupled system of transport equations. For this system, an approximate description is derived in the form of coupled damped wave equations and ultimately in the form of a scalar diffusion equation. The resulting diffusion coefficient is quite different from what one would get for a walk on straight lines with tumbling (as in bacterial motion). © 2011 Taylor & Francis.