Travelling waves modulated by subthreshold oscillations in networks of integrate-and-fire neurons
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908635970404352 |
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| author | Kerr, Henry D. J. Ashwin, Peter Wedgwood, Kyle C. A. |
| author_facet | Kerr, Henry D. J. Ashwin, Peter Wedgwood, Kyle C. A. |
| contents | Travelling waves of neural firing activity are observed in brain tissue as a part of various sensory, motor and cognitive processes. They represent an object of major interest in the study of excitable networks, with analysis conducted in both neural field models and spiking neuronal networks. The latter class exposes the single-neuron dynamics directly, allowing us to study the details of their influence upon network-scale behaviour. Here we present a study of a laterally-inhibited network of leaky integrate-and-fire neurons modulated by a slow voltage-gated ion channel that acts as a linear adaptation variable. As the strength of the ion channel increases, we find that its interaction with the lateral inhibition increases wave speeds. The ion channel can enable subthreshold oscillations, with the intervals between the firing events of loosely-coupled travelling wave solutions structured around the neuron's natural period. These subthreshold oscillations also enable the occurrence of codimension-2 grazing bifurcations; along with the emergence of fold bifurcations along wave solution branches, the slow ion channel introduces a variety of intermediate structures in the solution space. These point towards further investigation of the role neighbouring solution branches play in the behaviour of waves forced across bifurcations, which we illustrate with the aid of simulations using a novel root-finding algorithm designed to handle uncertainty over the existence of firing solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Travelling waves modulated by subthreshold oscillations in networks of integrate-and-fire neurons Kerr, Henry D. J. Ashwin, Peter Wedgwood, Kyle C. A. Neurons and Cognition 92B20 (Primary) 92C42, 65D15, 65P30 (Secondary) Travelling waves of neural firing activity are observed in brain tissue as a part of various sensory, motor and cognitive processes. They represent an object of major interest in the study of excitable networks, with analysis conducted in both neural field models and spiking neuronal networks. The latter class exposes the single-neuron dynamics directly, allowing us to study the details of their influence upon network-scale behaviour. Here we present a study of a laterally-inhibited network of leaky integrate-and-fire neurons modulated by a slow voltage-gated ion channel that acts as a linear adaptation variable. As the strength of the ion channel increases, we find that its interaction with the lateral inhibition increases wave speeds. The ion channel can enable subthreshold oscillations, with the intervals between the firing events of loosely-coupled travelling wave solutions structured around the neuron's natural period. These subthreshold oscillations also enable the occurrence of codimension-2 grazing bifurcations; along with the emergence of fold bifurcations along wave solution branches, the slow ion channel introduces a variety of intermediate structures in the solution space. These point towards further investigation of the role neighbouring solution branches play in the behaviour of waves forced across bifurcations, which we illustrate with the aid of simulations using a novel root-finding algorithm designed to handle uncertainty over the existence of firing solutions. |
| title | Travelling waves modulated by subthreshold oscillations in networks of integrate-and-fire neurons |
| topic | Neurons and Cognition 92B20 (Primary) 92C42, 65D15, 65P30 (Secondary) |
| url | https://arxiv.org/abs/2511.05232 |