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Oscillations in a Fully Connected Network of Leaky Integrate-and-Fire Neurons with a Poisson Spiking Mechanism

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Abstract

Understanding the mechanisms that lead to oscillatory activity in the brain is an ongoing challenge in computational neuroscience. Here, we address this issue by considering a network of excitatory neurons with Poisson spiking mechanism. In the mean-field formalism, the network’s dynamics can be successfully rendered by a nonlinear dynamical system. The stationary state of the system is computed and a perturbation analysis is performed to obtain an analytical characterization for the occurrence of instabilities. Taking into account two parameters of the neural network, namely synaptic coupling and synaptic delay, we obtain numerically the bifurcation line separating the non-oscillatory from the oscillatory regime. Moreover, our approach can be adapted to incorporate multiple interacting populations.

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Author notes

  1. Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu contributed equally to this work.

Authors and Affiliations

  1. Department of Cognitive Studies, Ecole Normale Supérieure, rue d’Ulm, 75005, Paris, France

    Grégory Dumont

  2. INRIA team Carmen, INRIA Bordeaux Sud-Ouest, Avenue de la Vieille Tour, 33405, Talence cedex, France

    Jacques Henry

  3. Department of Mathematics and Informatics, “Gheorghe Asachi” Technical University of Iaşi, Carol I 11, 700506, Iaşi, Romania

    Carmen Oana Tarniceriu

  4. The Institute of Interdisciplinary Research, Department of Exact Sciences and Natural Sciences, “Alexandru Ioan Cuza” University of Iaşi, Alexandru Lăpuşneanu 26, 700057, Iaşi, Romania

    Carmen Oana Tarniceriu

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  1. Grégory Dumont
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  2. Jacques Henry
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  3. Carmen Oana Tarniceriu
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Correspondence to Carmen Oana Tarniceriu.

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Dumont, G., Henry, J. & Tarniceriu, C.O. Oscillations in a Fully Connected Network of Leaky Integrate-and-Fire Neurons with a Poisson Spiking Mechanism. J Nonlinear Sci 34, 18 (2024). https://doi.org/10.1007/s00332-023-09995-x

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