Publication

Synchronization and Graph Topology

Martin Hasler, Igor Belykh
2005
Journal Articles

Abstract

This paper clarifies the relation between synchronization and graph topology. Applying the Connection Graph Stability method developed by Belykh et al. [2004a] to the study of synchronization in networks of coupled oscillators, we show which graph properties matter for synchronization. In particular, while we explicitly link the stability of synchronization with the average path length for a wide class of coupling graphs, we prove by a simple argument that the average path length is not always the crucial quantity for synchronization. We also show that synchronization in scale-free networks can be described by means of regular networks with a star-like coupling structure. Finally, by considering an example of coupled Hindmarsh–Rose neuron models, we demonstrate how global stability of synchronization depends on the parameters of the individual oscillator.

Official source

https://infoscience.epfl.ch/entities/publication/ebe03b8d-b971-418a-9f22-5170c18945e3

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Martin Hasler, Igor Belykh
2005
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ebe03b8d-b971-418a-9f22-5170c18945e3

About this result

Related concepts (20)

Complex network

In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.

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