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Clustering in Small Networks of Excitatory Neurons with Heterogeneous Coupling Strengths

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Abstract

Excitatory coupling with a slow rise time destabilizes synchrony between coupled neurons. Thus, the fully synchronous state is usually unstable in networks of excitatory neurons. Phase-clustered states, in which neurons are divided into multiple synchronized clusters, have also been found unstable in numerical studies of excitatory networks in the presence of noise. The question arises as to whether synchrony is possible in networks of neurons coupled through slow, excitatory synapses. In this paper, we show that robust, synchronous clustered states can occur in such networks. The effects of non-uniform distributions of coupling strengths are explored. Conditions for the existence and stability of clustered states are derived analytically. The analysis shows that a multi-cluster state can be stable in excitatory networks if the overall interactions between neurons in different clusters are stabilizing and strong enough to counter-act the destabilizing interactions between neurons within each cluster. When heterogeneity in the coupling strengths strengthens the stabilizing inter-cluster interactions and/or weakens the destabilizing in-cluster interactions, robust clustered states can occur in excitatory networks of all known model neurons. Numerical simulations were carried out to support the analytical results.

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Authors and Affiliations

  1. Departments of Mathematics and Zoology, University of British Columbia, Vancouver, BC, Canada, V6T 1Z2

    Yue-Xian Li

  2. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z2

    Yu-qing Wang

  3. Departments of Mathematics and Pharmacology & Therapeutics, University of British Columbia, Vancouver, BC, Canada, V6T 1Z2

    Robert Miura

  4. Departments of Mathematical Sciences and Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Robert Miura

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  1. Yue-Xian Li
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  2. Yu-qing Wang
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  3. Robert Miura
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Li, YX., Wang, Yq. & Miura, R. Clustering in Small Networks of Excitatory Neurons with Heterogeneous Coupling Strengths. J Comput Neurosci 14, 139–159 (2003). https://doi.org/10.1023/A:1021902717424

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