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Nonlinear Dynamics New Directions pp 1–28Cite as

Patterns of Synchrony in Neuronal Networks: The Role of Synaptic Inputs

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Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 12))

Abstract

We study the role of network architecture and synaptic inputs in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. Through analysis and numerics, we show that the stability of the completely synchronous state, representing the largest cluster, only depends on the number of synaptic inputs each neuron receives, independent from all other details of the network topology. We also give a simple combinatorial algorithm that finds synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We address the asymptotic stability of cluster synchronization in excitatory networks of bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.

Dedicated to Valentin S. Afraimovich on the occasion of his 65th birthday

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Acknowledgment

This work was supported by the National Science Foundation under Grant DMS-1009744, the GSU Brains and Behavior program, and RFFI Grants N 2100-065268 and N 09-01-00498-a (to I.B.).

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Authors and Affiliations

  1. Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, GA, 30303, USA

    Igor Belykh

  2. School of Computer and Communication Sciences, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 14, 1015, Lausanne, Switzerland

    Martin Hasler

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  1. Igor Belykh
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Correspondence to Igor Belykh .

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Editors and Affiliations

  1. Autonomous University of San Luis Potosí, San Luis Potosi, Mexico

    Hernán González-Aguilar

  2. Autonomous University of San Luis Potosí, San Luis Potosi, Mexico

    Edgardo Ugalde

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Belykh, I., Hasler, M. (2015). Patterns of Synchrony in Neuronal Networks: The Role of Synaptic Inputs. In: González-Aguilar, H., Ugalde, E. (eds) Nonlinear Dynamics New Directions. Nonlinear Systems and Complexity, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-09864-7_1

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  • DOI: https://doi.org/10.1007/978-3-319-09864-7_1

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