Math Biology Seminar: Biological aggregation patterns and the role of social interactions

  • Date: 10/22/2009
Chad Higdon-Topaz (Macalester College)

University of British Columbia


Biological aggregations such as insect swarms, bird flocks, and fish
schools are arguably some of the most common and least understood
patterns in nature. In this talk, I will discuss recent work on
swarming models, focusing on the connection between inter-organism
social interactions and properties of macroscopic swarm patterns. The
first model is a conservation-type partial integrodifferential equation
(PIDE). Social interactions of incompressible form lead to vortex-like
swarms. The second model is a high-dimensional ODE description of
locust groups. The statistical-mechanical properties of the
attractive-repulsive social interaction potential control whether or
not individuals form a rolling migratory swarm pattern similar to those
observed in nature. For the third model, we again return to a
conservation-type PIDE and, via long- and short-wave analysis,
determine general conditions that social interactions must satisfy for
the population to asymptotically spread, contract, or reach steady


2:00pm-3:00pm, WMAX 110

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