Программный комплекс FrOsFHN для количественного и качественного анализа дробного осциллятора ФитцХью-Нагумо, с переменной памятью

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.