Handbook of Graphs and Networks 2002
DOI: 10.1002/3527602755.ch16
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Graph theory and the evolution of autocatalytic networks

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 interac… Show more

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Cited by 31 publications
(31 citation statements)
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“…In particular, topological analysis allows for making judgments regarding stability, vulnerability to damage, mechanisms of self-repair, scenarios of self-organization and other properties. Moreover, some versions of the network dynamics are capable of elucidating the mechanisms of prebiotic evolution through spontaneous birth of small autocatalytic molecular sets followed by rapid self-organization into complex biomolecular structures [88]. In general, topological analysis is capable of elucidating systemic properties , that is, the ones that characterize the network’s global behavior .…”
Section: Mathematical Descriptions Of Biochemical Networkmentioning
confidence: 99%
“…In particular, topological analysis allows for making judgments regarding stability, vulnerability to damage, mechanisms of self-repair, scenarios of self-organization and other properties. Moreover, some versions of the network dynamics are capable of elucidating the mechanisms of prebiotic evolution through spontaneous birth of small autocatalytic molecular sets followed by rapid self-organization into complex biomolecular structures [88]. In general, topological analysis is capable of elucidating systemic properties , that is, the ones that characterize the network’s global behavior .…”
Section: Mathematical Descriptions Of Biochemical Networkmentioning
confidence: 99%
“…Jain and Krishna [52] investigated the evolution of directed graphs and the emergence of self-reinforcing autocatalytic networks of interaction. They identified the attractors in these networks and demonstrated a diverse range of behaviors from the creation of structural complexity to its collapse and permanent loss.…”
Section: Discussionmentioning
confidence: 99%
“…The Lotka–Volterra equation describes an astounding number of possible scenarios of behavior, including various forms of stability, instability, periodicity and chaos [25,26]. In particular, mathematical analysis has revealed the explicit conditions under which multiple attractors will exist in a high-dimensional Lotka–Volterra system, resulting in multistability [27]. …”
Section: A New Scientific Connection: Medicine Meets Ecological Theorymentioning
confidence: 99%