%0 Journal Article %1 citeulike:566295 %A Jain, Sanjay %A Krishna, Sandeep %D 2002 %K emergence artificialchemistry topology graphteory networks %T Graph Theory and the Evolution of Autocatalytic Networks %U http://arxiv.org/abs/nlin.AO/0210070 %X 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.

@article{citeulike:566295, 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.}, added-at = {2006-07-26T16:57:36.000+0200}, author = {Jain, Sanjay and Krishna, Sandeep}, biburl = {https://www.bibsonomy.org/bibtex/2c31b8377100d2385c605a6dbaf0dbf5c/pietrosperoni}, citeulike-article-id = {566295}, eprint = {nlin.AO/0210070}, interhash = {1584d743dbd8f3c6ef7b8490a81318cb}, intrahash = {c31b8377100d2385c605a6dbaf0dbf5c}, keywords = {emergence artificialchemistry topology graphteory networks}, month = Oct, priority = {3}, timestamp = {2009-01-07T08:09:00.000+0100}, title = {Graph Theory and the Evolution of Autocatalytic Networks}, url = {http://arxiv.org/abs/nlin.AO/0210070}, year = 2002 }