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Peer-reviewedCC BY 4.0PLOS One

Experimental and theoretical investigation of parameter-driven stability and chaos in a non-linear neuron circuit model

  • Haiqa Ehsan1
  • Haseeba Sajjad2
  • Adil Jhangeer3
  • Lubomír Říha4
4 affiliations
  1. 1IT4Innovations, VSB-Technical University of Ostrava, Ostrava-Poruba, Czech Republic
  2. 2Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, Ostrava-Poruba, Czech Republic
  3. 3Center for Theoretical Physics, Khazar University, Baku, Azerbaijan, Azerbaijan
  4. 4Department of Computer Engineering, Biruni University, Istanbul, Turkey
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Abstract

In this study, a neural-inspired electronic circuit consisting of a pressure-sensitive FitzHugh-Nagumo model with the addition of a piezoelectric bi-membrane and two capacitors is explored. The governing equations are obtained analytically from Kirchhoff’s laws, which represent the nonlinear interactions, oscillatory response, and stability of the circuit. A perturbation term is added to investigate the deviations from the system potential, and the transitions in the system are studied under the assumption of the model. By applying statistical methods and eigenvalue analysis, the parameter space is systematically subdivided and examined, and the results show that the behavior of the system is dominated by divergent behavior, although some periodic oscillatory behavior is seen in certain regions. This highlights the importance of initial conditions and parameter selection on the behavior of the system, which are essential to obtaining stable behavior and developing an efficient control design. Furthermore, an ensemble-size sensitivity analysis is performed to verify the robustness and convergence of the statistical characterization across different numbers of initial conditions. Phase disturbance plots, power spectrum density plots, attractor reconstruction plots, return maps, and noise detection maps are used to analyze the system dynamics. In addition, a multi-sum (multi-parameter interaction) diagram is created to depict the interactions between circuit variables and the overall system behavior.

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Cite

BibTeXRIS
BibTeX
@article{ehsan2026experimental,
  title = {{Experimental and theoretical investigation of parameter-driven stability and chaos in a non-linear neuron circuit model}},
  author = {Haiqa Ehsan and Haseeba Sajjad and Adil Jhangeer and Lubomír Říha},
  journal = {PLOS One},
  year = {2026},
  month = nov,
  doi = {10.1371/journal.pone.0360729},
  url = {https://doi.org/10.1371/journal.pone.0360729},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Experimental and theoretical investigation of parameter-driven stability and chaos in a non-linear neuron circuit model
AU  - Haiqa Ehsan
AU  - Haseeba Sajjad
AU  - Adil Jhangeer
AU  - Lubomír Říha
PY  - 2026
DA  - 2026/11/06
JO  - PLOS One
DO  - 10.1371/journal.pone.0360729
UR  - https://doi.org/10.1371/journal.pone.0360729
AB  - In this study, a neural-inspired electronic circuit consisting of a pressure-sensitive FitzHugh-Nagumo model with the addition of a piezoelectric bi-membrane and two capacitors is explored. The governing equations are obtained analytically from Kirchhoff’s laws, which represent the nonlinear interactions, oscillatory response, and stability of the circuit. A perturbation term is added to investigate the deviations from the system potential, and the transitions in the system are studied under the assumption of the model. By applying statistical methods and eigenvalue analysis, the parameter space is systematically subdivided and examined, and the results show that the behavior of the system is dominated by divergent behavior, although some periodic oscillatory behavior is seen in certain regions. This highlights the importance of initial conditions and parameter selection on the behavior of the system, which are essential to obtaining stable behavior and developing an efficient control design. Furthermore, an ensemble-size sensitivity analysis is performed to verify the robustness and convergence of the statistical characterization across different numbers of initial conditions. Phase disturbance plots, power spectrum density plots, attractor reconstruction plots, return maps, and noise detection maps are used to analyze the system dynamics. In addition, a multi-sum (multi-parameter interaction) diagram is created to depict the interactions between circuit variables and the overall system behavior.
SN  - 1932-6203
ER  -