Structure of a randomly grown 2-d network

Fioralba Ajazi; George M Napolitano; Tatyana Turova; Izbassar Zaurbek

doi:10.1016/j.biosystems.2015.09.002

Structure of a randomly grown 2-d network

Biosystems. 2015 Oct:136:105-12. doi: 10.1016/j.biosystems.2015.09.002. Epub 2015 Sep 14.

Authors

Fioralba Ajazi¹, George M Napolitano², Tatyana Turova³, Izbassar Zaurbek⁴

Affiliations

¹ 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.
² Department of Mathematical Statistics, Faculty of Science, Lund University, Sölvegatan 18, 22100 Lund, Sweden. Electronic address: gmn@maths.lth.se.
³ 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.
⁴ Department of Mathematical Statistics, Faculty of Science, Lund University, Sölvegatan 18, 22100 Lund, Sweden.

PMID: 26375356
DOI: 10.1016/j.biosystems.2015.09.002

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.

Keywords: Random graphs; Randomly grown network.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Animals
Computer Simulation
Feedback, Physiological / physiology
Humans
Models, Neurological*
Models, Statistical*
Nerve Net / physiology*
Neuronal Plasticity / physiology*
Neurons / physiology*
Synaptic Transmission / physiology*