

Preprint 77/2008
Preferential attachment renders an evolving network of populations robust against crashes
Areejit Samal and Hildegard Meyer-Ortmanns
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Submission date: 31. Oct. 2008 (revised version: December 2008)
Pages: 17
published in: Physica / A, 388 (2009) 8, p. 1535-1545
DOI number (of the published article): 10.1016/j.physa.2008.12.045
Bibtex
PACS-Numbers: 89.75.Fb, 89.75.Hc, 87.23.kg
Keywords and phrases: complex networks, network evolution, population dynamics, selection, autocatalytic set
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Abstract:
We study a model for the evolution of chemical species under a
combination of population dynamics on a short time scale and a
selection mechanism on a larger time scale. Least fit nodes are
replaced by new nodes whose links are attached to the nodes of
the given network via preferential attachment.
In contrast to a random attachment of newly incoming nodes that
as used in previous work, this preferential attachment mechanism
accelerates the generation of a so-called autocatalytic set after
a start from a random geometry and the growth of this structure
until it saturates in a stationary phase in which the whole system
is an autocatalytic set. Moreover, the system in the stationary
phase becomes much more stable against crashes in the population
size as compared to random attachment. We explain in detail in
terms of graph theoretical notions which structure of the resulting
network is responsible for this stability. Essentially it is a
very dense core with many loops and less nodes playing the role of
a keystone that prevent crashes almost completely.