Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916745766240256 |
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| author | Pazó, Diego Cestnik, Rok |
| author_facet | Pazó, Diego Cestnik, Rok |
| contents | We report on an exact theory for ensembles of globally coupled, heterogeneous complex Riccati equations. A drastic dimensionality reduction to a few ordinary differential equations is achieved for Lorentzian heterogeneity. By applying this technique, we obtain low-dimensional firing-rate equations for populations of spiking neurons with a clustered substructure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure Pazó, Diego Cestnik, Rok Neurons and Cognition Exactly Solvable and Integrable Systems We report on an exact theory for ensembles of globally coupled, heterogeneous complex Riccati equations. A drastic dimensionality reduction to a few ordinary differential equations is achieved for Lorentzian heterogeneity. By applying this technique, we obtain low-dimensional firing-rate equations for populations of spiking neurons with a clustered substructure. |
| title | Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure |
| topic | Neurons and Cognition Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.15537 |