A mathematical and experimental study of ant foraging line dynamics

Rossi, Louis F.
Johnson, Katie
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Department of Mathematical Sciences
In this article, we present a mathematical model coupled to an experimental study of ant foraging lines. Our laboratory experiments do not support the common traffic modeling assumption that ant densities and velocities are directly correlated. Rather, we find that higher order effects play a major role in observed behavior, and our model reflects this by including inertial terms in the evolution equation. A linearization of the resulting system yields left- and right-moving waves, in agreement with laboratory measurements. The linearized system depends upon two Froude numbers reflecting a ratio of the energy stored in the foraging line to the kinetic energy of the ants. Furthermore, the model predicts and the measurements support the existence of two distinct phase velocities.
Mathematical modeling , ant colony , self-organization , foraging lines