Leadership in Animal Group Motion: A Bifurcation Analysis

Benjamin Nabet, Naomi Ehrich Leonard, Iain D. Couzin and Simon A. Levin

Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, July 2006.
We present a low-dimensional, continuous model of a multi-agent system motivated by simulation studies on dynamics of decision making in animal groups in motion. Each individual moves at constant speed in the plane and adjusts its heading in response to relative headings of others in the population. Two subgroups of the population are informed such that individuals in each subgroup have a preferred direction of motion. The model exhibits stable solutions corresponding to compromise by individuals with conflicting preferences. We study the global phase space for the proposed model by computing equilibria and proving stability and bifurcations.

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