Non-stationary dynamics of interspike intervals in neuronal populations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914225175134208 |
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| author | Falorsi, Luca Vinci, Gianni V. Mattia, Maurizio |
| author_facet | Falorsi, Luca Vinci, Gianni V. Mattia, Maurizio |
| contents | We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the evolution of the full neuronal state, along with a one-dimensional hierarchy of equations for the moments of the inter-spike interval (ISI). The formalism allows us to characterize the time-dependent ISI distribution, even when the population is far from stationarity, such as under time-varying external input or during network oscillations. By performing a perturbative expansion around the stationary state, we also derive an analytic expression for the linear response of the ISI distribution to weak input modulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-stationary dynamics of interspike intervals in neuronal populations Falorsi, Luca Vinci, Gianni V. Mattia, Maurizio Disordered Systems and Neural Networks Neurons and Cognition We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the evolution of the full neuronal state, along with a one-dimensional hierarchy of equations for the moments of the inter-spike interval (ISI). The formalism allows us to characterize the time-dependent ISI distribution, even when the population is far from stationarity, such as under time-varying external input or during network oscillations. By performing a perturbative expansion around the stationary state, we also derive an analytic expression for the linear response of the ISI distribution to weak input modulations. |
| title | Non-stationary dynamics of interspike intervals in neuronal populations |
| topic | Disordered Systems and Neural Networks Neurons and Cognition |
| url | https://arxiv.org/abs/2512.23922 |