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arXiv · 2608.03454

Analysis of inverse stochastic resonance: Effects of neural excitability and timescale separation

Marius E. Yamakou·Torben Krüger·Hermann Schulz-Baldes
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Abstract

We analyze inverse stochastic resonance (ISR) in a bistable FitzHugh--Nagumo neuron driven by additive noise in the voltage variable, focusing on how neural excitability and timescale separation regulate the noise-induced modulation of spiking activity. A codimension-two bifurcation analysis identifies a narrow bistable region in which a stable fixed point and a stable limit cycle coexist, separated by an unstable periodic orbit. Finite-time Monte Carlo simulations show that the occupation of the limit-cycle basin may appear to depend on the initial basin when rare transitions are not fully resolved. We prove that this dependence is not asymptotic: the stochastic system admits a unique invariant probability measure, so long-time firing statistics are independent of the initial basin of attraction. The parameter dependence of ISR is characterized by quasi-potential barriers computed with a geometric minimum action method for the degenerate noise. The difference between the limit-cycle and fixed-point quasi-potentials partitions the bistable wedge into two escape-dominated regimes. A reduced metastable two-state Markov approximation yields a weak-noise formula for the limit-cycle basin occupation probability, a sign criterion for genuine ISR, and a semiquantitative prediction of the ISR-minimizing noise amplitude. In the fitted regime with a negative effective exponent, a genuine ISR minimum occurs only when the limit-cycle quasi-potential exceeds that of the fixed point. These results provide an escape-balance mechanism linking intrinsic neuronal parameters to asymptotic noise-induced spike suppression.

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Marius E. Yamakou, Torben Krüger, Hermann Schulz-Baldes. 2026-08-04. Analysis of inverse stochastic resonance: Effects of neural excitability and timescale separation. https://arxiv.org/abs/2608.03454

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