Presenter: Nour Riman
Time: 3:30 PM, Monday July 22nd
Location: Thackeray Hall 427
Title: The Dynamics of Bilateral Olfactory Search and Navigation
Committee: Brent Doiron, Bard Ermentrout, Nathan Urban
Animals use olfactory cues to navigate through their environment in order to find food, encounter mates, avoid predators and locate their home. We want to study the strategies animals use to localize odor sources and follow odor trails, and the neural circuitry that mediates this odor-driven behavior. Here, we present a mathematical analysis of 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.