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Structure and dynamics: The transition from nonequilibrium in integrate-and-fire dynamics

Lookup NU author(s): Professor Marcus Kaiser

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Abstract

The transient and equilibrium properties of dynamics unfolding in complex systems can depend critically on specific topological features of the underlying interconnections. In this work, we investigate such a relationship with respect to the integrate-and-fire dynamics emanating from a source node and an extended network model that allows control of the small-world feature as well as the length of the long-range connections. A systematic approach to investigate the local and global correlations between structural and dynamical features of the networks was adopted that involved extensive simulations (one and a half million cases) so as to obtain two-dimensional correlation maps. Smooth, but diverse surfaces of correlation values were obtained in all cases. Regarding the global cases, it has been verified that the onset avalanche time (but not its intensity) can be accurately predicted from the structural features within specific regions of the map (i.e. networks with specific structural properties). The analysis at local level revealed that the dynamical features before the avalanches can also be accurately predicted from structural features. This is not possible for the dynamical features after the avalanches take place. This is so because the overall topology of the network predominates over the local topology around the source at the stationary state.


Publication metadata

Author(s): Comin CH, Batista JLB, Viana MP, Costa LD, Travencolo BAN, Kaiser M

Publication type: Article

Publication status: Published

Journal: International Journal of Bifurcation and Chaos

Year: 2012

Volume: 22

Issue: 7

Print publication date: 01/07/2012

ISSN (print): 0218-1274

ISSN (electronic): 1793-6551

Publisher: World Scientific Publishing Co Pte Ltd

URL: http://dx.doi.org/10.1142/S021812741250174X

DOI: 10.1142/S021812741250174X


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