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Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks

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Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional network. A fundamental question in the analysis of complex systems concerns the relation between functional and structural networks. Using synchronisation as a paradigm for network functionality, we study the dynamics of cluster formation in functional networks. We show that the functional network can drastically differ from the structural network. We uncover the mechanism driving these bifurcations by obtaining necessary conditions for modular synchronisation.

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Notes

  1. 1.

    We see the equation as a parametric equation in the same spirit as the master stability function approach [3, 21, 24], hence we omit the subindex that explicitly shows the dependence on the node.

  2. 2.

    Under certain conditions, it is possible for two modules to synchronise and this is explored elsewhere such as [14].

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Authors and Affiliations

  1. University of Oxford, Oxford, UK

    Jake Stroud

  2. Department of Mathematics, Imperial College London, London, UK

    Mauricio Barahona & Tiago Pereira

Authors
  1. Jake Stroud
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  2. Mauricio Barahona
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  3. Tiago Pereira
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Corresponding author

Correspondence to Tiago Pereira .

Editor information

Editors and Affiliations

  1. Institute for Mathematical Research, University Putra Malaysia, Serdang, Malaysia

    Santo Banerjee

  2. Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy

    Lamberto Rondoni

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Stroud, J., Barahona, M., Pereira, T. (2015). Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks. In: Banerjee, S., Rondoni, L. (eds) Applications of Chaos and Nonlinear Dynamics in Science and Engineering - Vol. 4. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-17037-4_4

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