Pattern Formation via Scent-Marking
by
Mark Lewis
University of Alberta

In this talk I will propose a model for aggregating individuals through a random walk with bias toward scent marks which are made the individuals. The probability density function for an individual is given as the solution to a coupled system of partial/ordinary differential equations. This model differs from chemotaxis equations, where the scent marks can move. The analysis of the system, via application of an energy method, leads to distinct aggregations with abrupt edges. Applications will be made to the formation of territories, and connections will be made to ecological models for aggregating populations (eg. Turchin 1989, Journal of Animal Ecology 58: 75-100).

Date received: October 27, 2003