ANZIAM J.
48 (2006), 1-10
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Freely forming groups: Trying to be rare
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Uwe Grimm
Department of Mathematics
The Open University
Walton Hall
Milton Keynes MK7 6AA
UK
u.g.grimm@open.ac.uk
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Abstract
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A simple weakly frequency dependent model for
the dynamics of a population with a finite
number of types is proposed, based upon an
advantage of being rare. In the infinite
population limit, this model gives rise to a
non-smooth dynamical system that reaches its
globally stable equilibrium in finite time. This
dynamical system is sufficiently simple to
permit an explicit solution, built piecewise
from solutions of the logistic equation in
continuous time. It displays an interesting
tree-like structure of coalescing components.
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Australian Mathematical Publishing Association Inc.
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Australian MS
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