Graph Theory and the Evolution of Autocatalytic Networks
| dc.creator | Jain, Sanjay | |
| dc.creator | Krishna, Sandeep | |
| dc.date | 2002-10-30 | |
| dc.date.accessioned | 2026-07-07T05:34:23Z | |
| dc.date.available | 2026-07-07T05:34:23Z | |
| dc.description | 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. | |
| dc.description | 46 pages, 15 figures, to appear in "Handbook of Graphs and Networks", eds, S. Bornholdt and H. G. Schuster, John Wiley and VCH publishers | |
| dc.identifier | https://arxiv.org/abs/nlin/0210070 | |
| dc.identifier | http://arxiv.org/abs/nlin/0210070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80346 | |
| dc.subject | Adaptation and Self-Organizing Systems | |
| dc.title | Graph Theory and the Evolution of Autocatalytic Networks | |
| dc.type | text |