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Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure https://arxiv.org/abs/2503.15537 #qbioNC #nlinSI

Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure

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.

arXiv.org
March 22, 2025 at 3:25 AM · · feed2toot · 0 · 0 · 1
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