Abstract:Spiking neuronal networks connect cellular and synaptic mechanisms to collective activity, but estimating their long-time statistics often requires costly spike-by-spike simulation. We construct finite-state Markovian surrogates for neuronal populations with one- to three-dimensional intrinsic dynamics. A finite phase-space partition represents each population by its occupancy across single-neuron states, and the firing rate is defined uniformly as probability flux through model-specific spike transitions. We compare two closures: Type I enforces a stationary mean synaptic drive, whereas Type II retains its temporal evolution. In the leaky linear integrate-and-fire (LIF) benchmarks, the Type I estimator is accurate in temporally homogeneous cases but misses rate changes driven by synaptic timescales. In the synaptic-timescale sweep, the Type II estimator achieves small relative errors in most cases. Exponential integrate-and-fire (EIF) results exhibit an analogous qualitative pattern. FitzHugh--Nagumo (FHN) and reduced Hodgkin--Huxley (HH) examples extend the construction from one-dimensional threshold--reset dynamics to continuous trajectories in nonlinear two- and three-dimensional phase spaces. Together, these examples show how the finite-state construction generates model-dependent estimates of long-time state distributions and firing rates without resolving every neuron and spike.
From: Zhuo-Cheng Xiao [view email]
[v1]
Tue, 13 May 2025 06:04:02 UTC (11,041 KB)
[v2]
Wed, 14 May 2025 15:52:14 UTC (14,083 KB)
[v3]
Mon, 24 Aug 2026 07:06:21 UTC (12,501 KB)
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