  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.
