title: Structure of a randomly grown 2-d network.
abstract: We introduce a growing random network on a plane as a model of a growing neuronal network. The properties of the structure of the induced graph are derived. We compare our results with available data. In particular, it is shown that depending on the parameters of the model the system undergoes in time different phases of the structure. We conclude with a possible explanation of some empirical data on the connections between neurons.
authors.affiliation: Department of Mathematical Statistics, Faculty of Science, Lund University, Sölvegatan 18, 22100 Lund, Sweden; Neuroheuristic Research Group, Department of Information Systems, Faculty of Business and Economics, University of Lausanne, CH-1015, Switzerland.
authors.forename: Fioralba
authors.initials: F
authors.lastname: Ajazi
authors.affiliation: Department of Mathematical Statistics, Faculty of Science, Lund University, Sölvegatan 18, 22100 Lund, Sweden. Electronic address: gmn@maths.lth.se.
authors.forename: George M
authors.initials: GM
authors.lastname: Napolitano
authors.affiliation: Department of Mathematical Statistics, Faculty of Science, Lund University, Sölvegatan 18, 22100 Lund, Sweden; Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Institutskaja str., 142290 Pushchino, Moscow Region, Russia. Electronic address: tatyana@maths.lth.se.
authors.forename: Tatyana
authors.initials: T
authors.lastname: Turova
authors.affiliation: Department of Mathematical Statistics, Faculty of Science, Lund University, Sölvegatan 18, 22100 Lund, Sweden.
authors.forename: Izbassar
authors.initials: I
authors.lastname: Zaurbek
mesh_terms: D000818:Animals; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009473:Neuronal Plasticity / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D009435:Synaptic Transmission / Q000502:physiology*
keywords: Random graphs; Randomly grown network