Graph Theory and the Evolution of Autocatalytic Networks

dc.creatorJain, Sanjay
dc.creatorKrishna, Sandeep
dc.date2002-10-30
dc.date.accessioned2026-07-07T05:34:23Z
dc.date.available2026-07-07T05:34:23Z
dc.descriptionWe 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.description46 pages, 15 figures, to appear in "Handbook of Graphs and Networks", eds, S. Bornholdt and H. G. Schuster, John Wiley and VCH publishers
dc.identifierhttps://arxiv.org/abs/nlin/0210070
dc.identifierhttp://arxiv.org/abs/nlin/0210070
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80346
dc.subjectAdaptation and Self-Organizing Systems
dc.titleGraph Theory and the Evolution of Autocatalytic Networks
dc.typetext

Files

Collections