Sound detection through elliptical limit-cycle oscillations of the mosquito flagellum

Mosquitoes use their antennal flagella to detect the flight tones of each other, in order to identify and locate potential mates. The flagellum has been shown to actively oscillate in the absence of stimulus. These limit-cycle oscillations are believed to be used for the amplification of weak signals. Prior experimental measurements and theoretical models of the flagellum have considered only one axis of motion. However, the flagellum has two spacial degrees of freedom, resembling an inverted Foucault pendulum. In the current work, we show how these numerical models can be extended to include two spacial degrees of freedom by considering a circular configuration of coupled Hopf oscillators. We show that two different classes of models both predict that planar motion of the flagellum is unstable, and instead, the flagellum traces out an elliptical cone. Information about the sound source location and the sound intensity are encoded in the orientation and eccentricity, respectively, of the elliptical limit cycle. These theoretical results change our fundamental understanding of active flagellar dynamics and offer insight into how mosquitoes detect and localize faint sounds within noisy swarm environments.