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Bifurcation Analysis of a Sparse Neural Network with Cubic Topology

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Mathematical and Theoretical Neuroscience

Part of the book series: Springer INdAM Series ((SINDAMS,volume 24))

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Abstract

We study analytically the changes of dynamics of a firing-rate network model with cubic topology. The present study is performed by extending to this sparse network a formalism we previously developed for the bifurcation analysis of fully-connected circuits. In particular we prove that, unlike the fully-connected model, in the cubic network the neural activity may undergo spontaneous symmetry-breaking even if the network is composed exclusively of excitatory neurons. Moreover, while in the fully-connected topology the symmetry-breaking occurs through pitchfork bifurcations, in the excitatory cubic network it occurs through complex branching-point bifurcations with five branches. These results lead to the conclusion that the sparseness of the synaptic connections may increase the complexity of dynamics compared to dense networks.

∗ Diego Fasoli and Anna Cattani, these authors contributed equally to this work.

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Acknowledgements

This research was supported by the Autonomous Province of Trento, Call “Grandi Progetti 2012,” project “Characterizing and improving brain mechanisms of attention—ATTEND”.

The funders had no role in study design, data collection and analysis, decision to publish, interpretation of results, or preparation of the manuscript.

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    Authors and Affiliations

    1. Laboratory of Neural Computation, Center for Neuroscience and Cognitive Systems@UniTn, Istituto Italiano di Tecnologia, 38068, Rovereto, Italy

      Diego Fasoli, Anna Cattani & Stefano Panzeri

    2. Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, 08002, Barcelona, Spain

      Diego Fasoli

    Authors
    1. Diego Fasoli
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    2. Anna Cattani
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    3. Stefano Panzeri
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    Corresponding authors

    Correspondence to Diego Fasoli or Anna Cattani .

    Editor information

    Editors and Affiliations

    1. Environment Science and Policy, University of Milan, Milan, Italy

      Giovanni Naldi

    2. Department of Biomedical and Clinical Sciences, University of Milan, Milan, Italy

      Thierry Nieus

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    Fasoli, D., Cattani, A., Panzeri, S. (2017). Bifurcation Analysis of a Sparse Neural Network with Cubic Topology. In: Naldi, G., Nieus, T. (eds) Mathematical and Theoretical Neuroscience. Springer INdAM Series, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-68297-6_5

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