PMID: 15245198Jul 13, 2004Paper

Dynamical motifs: building blocks of complex dynamics in sparsely connected random networks

Physical Review Letters
Valentin P Zhigulin

Abstract

Spatiotemporal network dynamics is an emergent property of many complex systems that remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs-small subnetworks with periodic and chaotic dynamics. We simulate randomly connected neural networks and, with increasing density of connections, observe the transition from quiescence to periodic and chaotic dynamics. This transition is explained by the appearance of dynamical motifs in the structure of these networks. We also observe domination of periodic dynamics in simulations of spatially distributed networks with local connectivity and explain it by the absence of chaotic and the presence of periodic motifs in their structure.

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Citations

Apr 1, 2008·Proceedings of the National Academy of Sciences of the United States of America·Robert J Morgan, Ivan Soltesz
Mar 1, 2010·Journal of Biological Dynamics·Dewey T TaylorLauren E Pace
Sep 6, 2008·PLoS Computational Biology·Mark A KramerNancy J Kopell
Jul 14, 2012·PloS One·Zhaoyang ZhangGang Hu
Dec 3, 2008·Chaos·Thomas NowotnyMikhail I Rabinovich
Jun 3, 2008·Journal of Theoretical Biology·Mikhail V IvanchenkoMikhail I Rabinovich
Feb 29, 2008·Journal of Biological Engineering·Advait A ApteStephen S Fong
Oct 29, 2004·PLoS Biology·Olaf Sporns, Rolf Kötter
Nov 3, 2006·The Neuroscientist : a Review Journal Bringing Neurobiology, Neurology and Psychiatry·Danielle Smith Bassett, Ed Bullmore
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Antoine VenailleMikhail I Rabinovich
Jan 1, 2017·Applied Network Science·Marcus MärtensPiet Van Mieghem
Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dane Taylor, Juan G Restrepo
May 21, 2005·Physical Review Letters·Bosiljka TadićKrzysztof Kułakowski
Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rüdiger ZillmerAlessandro Torcini

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