A Planar Switching Neuron Shares Logarithmic First-Spike Latency with Its Three-Dimensional Parent But Not Its Onset Mechanism

Abstract

Can a reduced neuron model reproduce first-spike latency scaling while changing how a stimulus initiates sustained firing? We compare a piecewise-linear planar Neurosimilator with its three-dimensional parent. Both exhibit logarithmic latency dependence over the investigated input intervals, with different fitted coefficients. The mechanisms differ. In the parent, sustained spiking and a stable resting focus coexist in a spiking--rest bistability regime. An abrupt step accesses spiking, while slow stimulation can retain rest at the same final input. Its step-induced firing threshold is therefore an operational basin-access threshold below the saddle-node limit point, not a loss of equilibrium stability. In the planar model, the resting equilibrium instead reaches a switching boundary while its subthreshold eigenvalues remain negative. We derive the planar latency law from this boundary approach. The model generates repetitive excursions without an imposed reset and admits exact trajectories within six switching regions. Similar measured latency scaling thus coexists with different mechanisms of access to firing. Validating a reduced model's mechanism of excitability requires examination of stimulus protocol and attractor access alongside equilibrium structure and spike timing.