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PreprintCC BY 4.0arXiv

Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks

  • Jing Tian
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Abstract

In this study, we investigate continuous data assimilation for a class of partly diffusive FitzHugh--Nagumo neural networks with memristive feedback and linear synaptic coupling. The nudging algorithm implemented here only adds a feedback term to the membrane-potential equations, while the recovery and memductance variables remain unobserved. We obtain weighted energy estimates that give sufficient conditions for exponential convergence of the data-assimilated solution to the reference solution under full or coarse membrane potential observations. Moreover, we prove energy-class uniqueness in dimensions one and two. In dimension three, the uniqueness criterion is an L4 membrane-potential initial data. We also establish an observational-noise estimate for locally square-integrable forcing, yielding an asymptotic error bound when the noise energy is eventually bounded.

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Cite

BibTeXRIS
BibTeX
@misc{tian2026continuous,
  title = {{Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks}},
  author = {Jing Tian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.30480},
  eprint = {2609.30480},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30480},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks
AU  - Jing Tian
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.30480
UR  - https://arxiv.org/abs/2609.30480
AB  - In this study, we investigate continuous data assimilation for a class of partly diffusive FitzHugh--Nagumo neural networks with memristive feedback and linear synaptic coupling. The nudging algorithm implemented here only adds a feedback term to the membrane-potential equations, while the recovery and memductance variables remain unobserved. We obtain weighted energy estimates that give sufficient conditions for exponential convergence of the data-assimilated solution to the reference solution under full or coarse membrane potential observations. Moreover, we prove energy-class uniqueness in dimensions one and two. In dimension three, the uniqueness criterion is an L^4 membrane-potential initial data. We also establish an observational-noise estimate for locally square-integrable forcing, yielding an asymptotic error bound when the noise energy is eventually bounded.
ER  -