Supersymmetric Neuromorphic FitzHugh--Nagumo model
Abstract
We develop a supersymmetric spectral description of stochastic FitzHugh--Nagumo dynamics motivated by an effective antiferromagnetic neuromorphic model. A local normal-form reduction of the adopted tangential Néel-vector dynamics relates magnetic control parameters to fast activation and slow recovery coordinates. Freezing the recovery variable yields a one-dimensional Fokker--Planck equation with a quartic potential, whose similarity-transformed generator admits an exact supersymmetric factorization. The first nonzero relaxation eigenvalue is determined by the ground state of the partner operator; in the weak-noise bistable regime, it is approximated by the sum of the two interwell Kramers rates. Projecting the similarity-transformed probability density onto the two lowest modes defines a normalized auxiliary two-state amplitude. We derive its localized-basis coherence in terms of both the time-dependent basin populations and their equilibrium weights. Its maximum corresponds to equal normalized amplitude weights, which generally differ from equal basin populations. The fixed-recovery example exhibits a pronounced coherence pulse during monotonic relaxation without a spike. Conversely, the illustrated deterministic spiking trajectory repeatedly leaves the bistable domain and passes through regions with insufficient barrier separation, restricting the validity of the localized two-state approximation. These results connect stochastic relaxation spectra to an occupation-based coherence diagnostic and delimit its application to neuromorphic spiking. The diagnostic characterizes an auxiliary amplitude representation of classical stochastic dynamics and does not by itself establish microscopic quantum coherence.
Related
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- Analysis and stability of the FitzHugh-Nagumo system with rapidly oscillating Neumann boundary condition
- Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks
- Minimax solutions for FitzHugh-Nagumo systems with critical exponential growth
- Propagation failure in heterogeneous FitzHugh--Nagumo systems via coupled upper and lower solutions
BibTeX
@misc{maroulakos2026supersymmetric,
title = {{Supersymmetric Neuromorphic FitzHugh--Nagumo model}},
author = {D. Maroulakos and A. Wal and S. K. Mishra and Z. Toklikishvili and L. Chotorlishvili},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03312},
eprint = {2611.03312},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03312},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Supersymmetric Neuromorphic FitzHugh--Nagumo model
AU - D. Maroulakos
AU - A. Wal
AU - S. K. Mishra
AU - Z. Toklikishvili
AU - L. Chotorlishvili
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03312
UR - https://arxiv.org/abs/2611.03312
AB - We develop a supersymmetric spectral description of stochastic FitzHugh--Nagumo dynamics motivated by an effective antiferromagnetic neuromorphic model. A local normal-form reduction of the adopted tangential Néel-vector dynamics relates magnetic control parameters to fast activation and slow recovery coordinates. Freezing the recovery variable yields a one-dimensional Fokker--Planck equation with a quartic potential, whose similarity-transformed generator admits an exact supersymmetric factorization. The first nonzero relaxation eigenvalue is determined by the ground state of the partner operator; in the weak-noise bistable regime, it is approximated by the sum of the two interwell Kramers rates. Projecting the similarity-transformed probability density onto the two lowest modes defines a normalized auxiliary two-state amplitude. We derive its localized-basis coherence in terms of both the time-dependent basin populations and their equilibrium weights. Its maximum corresponds to equal normalized amplitude weights, which generally differ from equal basin populations. The fixed-recovery example exhibits a pronounced coherence pulse during monotonic relaxation without a spike. Conversely, the illustrated deterministic spiking trajectory repeatedly leaves the bistable domain and passes through regions with insufficient barrier separation, restricting the validity of the localized two-state approximation. These results connect stochastic relaxation spectra to an occupation-based coherence diagnostic and delimit its application to neuromorphic spiking. The diagnostic characterizes an auxiliary amplitude representation of classical stochastic dynamics and does not by itself establish microscopic quantum coherence.
ER -