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Nonlinear Sciences > Adaptation and Self-Organizing Systems

arXiv:nlin/0210070 (nlin)
[Submitted on 30 Oct 2002]

Title:Graph Theory and the Evolution of Autocatalytic Networks

Authors:Sanjay Jain (1,2,3,4), Sandeep Krishna (2) (1 - Department of Physics and Astrophysics, University of Delhi, Delhi. 2 - Centre for Theoretical Studies, Indian Institute of Science, Bangalore. 3 - Santa Fe Institute, Santa Fe. 4 - Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore.)
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Abstract: We give a self-contained introduction to the theory of directed graphs, leading up to the relationship between the Perron-Frobenius eigenvectors of a graph and its autocatalytic sets. Then we discuss a particular dynamical system on a fixed but arbitrary graph, that describes the population dynamics of species whose interactions are determined by the graph. The attractors of this dynamical system are described as a function of graph topology. Finally we consider a dynamical system in which the graph of interactions of the species coevolves with the populations of the species. We show that this system exhibits complex dynamics including self-organization of the network by autocatalytic sets, growth of complexity and structure, and collapse of the network followed by recoveries. We argue that a graph theoretic classification of perturbations of the network is helpful in predicting the future impact of a perturbation over short and medium time scales.
Comments: 46 pages, 15 figures, to appear in "Handbook of Graphs and Networks", eds, S. Bornholdt and H. G. Schuster, John Wiley and VCH publishers
Subjects: Adaptation and Self-Organizing Systems (nlin.AO)
Cite as: arXiv:nlin/0210070 [nlin.AO]
  (or arXiv:nlin/0210070v1 [nlin.AO] for this version)
  https://doi.org/10.48550/arXiv.nlin/0210070

Submission history

From: Sandeep Krishna [view email]
[v1] Wed, 30 Oct 2002 10:32:04 UTC (271 KB)
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