FracDynZe is a Computer Program for Studying the Dynamics of Cardiac Function using the Fractional Zeeman Oscillator

Parovik, R.I., Israyiljanova, G.S., Паровик, Р.И., Исрайилжанова, Г.С.

Ҳисоблаш ва амалий математика муаммолари · 2026-yil

Annotatsiya

This paper examines the dynamic modes of the fractional Zeeman oscillator. The fractional Zeeman oscillator is a system of two ordinary differential equations with fractional derivatives, understood in the Gerasimov-Caputo sense, for which local initial conditions are valid. The fractional Zeeman oscillator describes the dynamics of heart contractions using an electrochemical potential. Due to the nonlinearity of the fractional Zeeman oscillator, a numerical algorithm based on a nonlocal explicit finite-difference scheme was used to obtain a solution. The numerical algorithm was implemented in the FracDynZe computer program, written in Python in the PyCharm environment. The software package allows for visualization and saving of simulation results. This article describes the FracDynZe computer program, which implements a numerical algorithm for a nonlocal explicit finite-difference scheme. Using FracDynZe, test examples demonstrate that the numerical scheme has first-order accuracy. Examples and their visualizations are provided for various values of the Zeeman fractional oscillator parameters. The FracDynZe computer program can be supplemented with a module for the qualitative analysis of the Zeeman fractional oscillator. For example, this module can implement the ability to construct bifurcation diagrams for studying regular and chaotic regimes.

Maqola ma’lumotlari
MualliflarParovik, R.I., Israyiljanova, G.S., Паровик, Р.И., Исрайилжанова, Г.С.
JurnalҲисоблаш ва амалий математика муаммолари
NashriyotТошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази
ISSN2181-8460, 2181-046X
Nashr sanasi2026-05-02
Son2
Betlar5-15
TilIngliz
Ilmiy sohaTexnika
DOI10.71310/pcam.2_72.2026.01
Indeksga qo‘shilgan2026-08-27

DOI: 10.71310/pcam.2_72.2026.01 · Maqolaning asl sahifasi

Kalit so‘zlar

fractional derivatives, modeling, phase trajectory, stability, memory, python, numerical methods, дробные производные, моделирование, фазовая траектория, устойчивость, память, python, численные методы

Ilmiy soha

Texnika

Iqtibos keltirish

APAParovik, R.I., Israyiljanova, G.S., Паровик, Р.И., & Исрайилжанова, Г.С. (2026). FracDynZe is a Computer Program for Studying the Dynamics of Cardiac Function using the Fractional Zeeman Oscillator. Ҳисоблаш ва амалий математика муаммолари, (2), 5-15. https://doi.org/10.71310/pcam.2_72.2026.01
GOST (OAK)Parovik, R.I. va b. FracDynZe is a Computer Program for Studying the Dynamics of Cardiac Function using the Fractional Zeeman Oscillator // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 2. – P. 5-15. – DOI: 10.71310/pcam.2_72.2026.01.
MLAParovik, R.I., Israyiljanova, G.S., Паровик, Р.И., and Исрайилжанова, Г.С. “FracDynZe is a Computer Program for Studying the Dynamics of Cardiac Function using the Fractional Zeeman Oscillator.” Ҳисоблаш ва амалий математика муаммолари, (2), 5-15, 2026. https://doi.org/10.71310/pcam.2_72.2026.01
ChicagoParovik, R.I., Israyiljanova, G.S., Паровик, Р.И., and Исрайилжанова, Г.С. “FracDynZe is a Computer Program for Studying the Dynamics of Cardiac Function using the Fractional Zeeman Oscillator.” Ҳисоблаш ва амалий математика муаммолари, (2), 5-15 (2026). https://doi.org/10.71310/pcam.2_72.2026.01
HarvardParovik, R.I., Israyiljanova, G.S., Паровик, Р.И., and Исрайилжанова, Г.С (2026) ‘FracDynZe is a Computer Program for Studying the Dynamics of Cardiac Function using the Fractional Zeeman Oscillator’, Ҳисоблаш ва амалий математика муаммолари, (2), 5-15. https://doi.org/10.71310/pcam.2_72.2026.01
BibTeX
@article{parovikri2026,
  title = {FracDynZe is a Computer Program for Studying the Dynamics of Cardiac Function using the Fractional Zeeman Oscillator},
  author = {Parovik, R.I. and Israyiljanova, G.S. and Паровик, Р.И. and Исрайилжанова, Г.С.},
  journal = {Ҳисоблаш ва амалий математика муаммолари},
  year = {2026},
  number = {2},
  pages = {5-15},
  doi = {10.71310/pcam.2_72.2026.01},
  url = {https://doi.org/10.71310/pcam.2_72.2026.01}
}

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