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Article overview
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Graph Theory and the Evolution of Autocatalytic Networks | | Sanjay Jain
; Sandeep Krishna
; | | Date: |
30 Oct 2002 | | Subject: | Adaptation and Self-Organizing Systems | nlin.AO | | Affiliation: | 1,2,3,4) and Sandeep Krishna (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 Advance | | 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. | | Source: | arXiv, nlin.AO/0210070 | | Services: | Forum | Review | PDF | Favorites | |
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