The Dynamics of Bilateral Olfactory Search and Navigation

TL;DR

This paper models and analyzes the dynamics of bilateral olfactory navigation, revealing fixed points, multi-stability, and complex behaviors like chaos in different odor landscapes, enhancing understanding of animal odor-guided movement.

Contribution

It introduces a mathematical model of bilateral olfactory navigation with analytical reductions, exploring diverse behaviors across various odor landscape geometries.

Findings

Fixed points in infinite trail landscapes

Multi-stability and limit cycles in radial landscapes

Chaotic dynamics in complex odor environments

Abstract

Animals use stereo sampling of odor concentration to localize sources and follow odor trails. We analyze the dynamics of a bilateral model that depends on the simultaneous comparison between odor concentrations detected by left and right sensors. The general model consists of three differential equations for the positions in the plane and the heading. When the odor landscape is an infinite trail, then we reduce the dynamics to a planar system whose dynamics have just two fixed points. Using an integrable approximation (for short sensors) we estimate the basin of attraction. In the case of a radially symmetric landscape, we again can reduce the dynamics to a planar system, but the behavior is considerably richer with multi-stability, isolas, and limit cycles. As in the linear trail case, there is also an underlying integrable system when the sensors are short. In odor landscapes that consist of multiple spots and trail segments, we find periodic and chaotic dynamics and characterize the behavior on trails with gaps and that turn corners.