FrOsFHN Software Package for Quantitative and Qualitative Analysis of the FitzHugh-Nagumo Fractional Oscillator with Variable Memory

Alimova, N.B., Parovik, R.I., Алимова, Н.Б., Паровик, Р.И.

Ҳисоблаш ва амалий математика муаммолари · 2026-yil

Annotatsiya

This article describes and provides examples of the FrOsFHN software package for the quantitative and qualitative analysis of a nonlinear FitzHugh-Nagumo oscillator with variable memory (the fractional FitzHugh-Nagumo oscillator (FrOsFHN)). Variable memory was taken into account in the FitzHugh-Nagumo oscillator model equation using fractional-order derivatives of the Gerasimov-Caputo type with respect to time. The quantitative analysis in the software package was implemented based on a numerical algorithm for a nonlocal explicit finite-difference scheme of first-order accuracy, and the qualitative analysis was implemented using algorithms for visualizing the numerical solution in the form of oscillograms, phase trajectories, and bifurcation diagrams. To conduct the quantitative analysis, the user was able to select the functional dependence of the fractional derivative orders on time: a linear decreasing function, a trigonometric function, or a decreasing exponential function. To construct bifurcation diagrams, we implemented the ability to consider a parallel version of the algorithm in addition to the sequential version, leveraging the computing resources of the computer’s central processor. The software package also features the ability to save calculations to a text file, as well as result graphs. The software package was written in Python using the PyCharm environment.

Maqola ma’lumotlari
MualliflarAlimova, N.B., Parovik, R.I., Алимова, Н.Б., Паровик, Р.И.
JurnalҲисоблаш ва амалий математика муаммолари
NashriyotТошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази
ISSN2181-8460, 2181-046X
Nashr sanasi2026-01-11
Son6
Betlar5-17
TilIngliz
Ilmiy sohaTexnika
DOI10.71310/pcam.6_70.2025.01
Indeksga qo‘shilgan2026-08-27

DOI: 10.71310/pcam.6_70.2025.01 · Maqolaning asl sahifasi

Kalit so‘zlar

FitzHugh-Nagumo fractional oscillator, oscillograms, phase trajectories, nonlocal explicit finite-difference scheme, algorithms, Python, PyCharm, bifurcation diagram, дробный осциллятор ФитцХью-Нагумо, осциллограммы, фазовые траектории, нелокальная явная конечно-разностная схема, алгоритмы, Python, PyCharm, бифуркационная диаграмма

Ilmiy soha

Texnika

Iqtibos keltirish

APAAlimova, N.B., Parovik, R.I., Алимова, Н.Б., & Паровик, Р.И. (2026). FrOsFHN Software Package for Quantitative and Qualitative Analysis of the FitzHugh-Nagumo Fractional Oscillator with Variable Memory. Ҳисоблаш ва амалий математика муаммолари, (6), 5-17. https://doi.org/10.71310/pcam.6_70.2025.01
GOST (OAK)Alimova, N.B. va b. FrOsFHN Software Package for Quantitative and Qualitative Analysis of the FitzHugh-Nagumo Fractional Oscillator with Variable Memory // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 6. – P. 5-17. – DOI: 10.71310/pcam.6_70.2025.01.
MLAAlimova, N.B., Parovik, R.I., Алимова, Н.Б., and Паровик, Р.И. “FrOsFHN Software Package for Quantitative and Qualitative Analysis of the FitzHugh-Nagumo Fractional Oscillator with Variable Memory.” Ҳисоблаш ва амалий математика муаммолари, (6), 5-17, 2026. https://doi.org/10.71310/pcam.6_70.2025.01
ChicagoAlimova, N.B., Parovik, R.I., Алимова, Н.Б., and Паровик, Р.И. “FrOsFHN Software Package for Quantitative and Qualitative Analysis of the FitzHugh-Nagumo Fractional Oscillator with Variable Memory.” Ҳисоблаш ва амалий математика муаммолари, (6), 5-17 (2026). https://doi.org/10.71310/pcam.6_70.2025.01
HarvardAlimova, N.B., Parovik, R.I., Алимова, Н.Б., and Паровик, Р.И (2026) ‘FrOsFHN Software Package for Quantitative and Qualitative Analysis of the FitzHugh-Nagumo Fractional Oscillator with Variable Memory’, Ҳисоблаш ва амалий математика муаммолари, (6), 5-17. https://doi.org/10.71310/pcam.6_70.2025.01
BibTeX
@article{alimovanb2026,
  title = {FrOsFHN Software Package for Quantitative and Qualitative Analysis of the FitzHugh-Nagumo Fractional Oscillator with Variable Memory},
  author = {Alimova, N.B. and Parovik, R.I. and Алимова, Н.Б. and Паровик, Р.И.},
  journal = {Ҳисоблаш ва амалий математика муаммолари},
  year = {2026},
  number = {6},
  pages = {5-17},
  doi = {10.71310/pcam.6_70.2025.01},
  url = {https://doi.org/10.71310/pcam.6_70.2025.01}
}

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