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Original Research ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Appl. Math. Stat. | doi: 10.3389/fams.2019.00052

Synchronization patterns in modular neuronal networks: a case study of C. elegans

  • 1Technische Universität Berlin, Germany
  • 2Bernstein Center for Computational Neuroscience Berlin (NNCN), Germany
  • 3University of Namur, Belgium
  • 4University College Cork, Ireland
  • 5Crete Center for Quantum Complexity and Nanotechnology, Department of Physics, University of Crete, Greece

We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities.

Keywords: synchronization, multilayer network, chimera state, neuronal oscillators, Metastability, community detection

Received: 15 Dec 2018; Accepted: 07 Oct 2019.

Copyright: © 2019 Pournaki, Merfort, Ruiz, Kouvaris, Hövel and Hizanidis. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Philipp Hövel, University College Cork, Cork, Ireland, philipp.hoevel@ucc.ie