ABMSelkovFracSim 2.0 software package for quantitative and qualitative analysis of the Selkov fractional oscillator

This article presents a new version of the ABMSelkovFracSim software package (ABMSelkovFracSim 2.0), written in the Python programming language. This package includes a software module for constructing bifurcation diagrams for the qualitative analysis of the oscillatory modes of the Selkov fractional oscillator. The Selkov fractional oscillator is a Cauchy problem for a system of two coupled nonlinear ordinary differential equations with Gerasimov-Caputo derivatives of fractional order variables and non-constant coefficients. Using the Adams-Bashforth-Multon numerical algorithm, this software package not only constructs oscillograms and phase trajectories based on the values and functions of key parameters of the model equations, as previously implemented in the ABMSelkovFracSim software package, but also calculates bifurcation diagrams for the oscillatory modes of the Selkov fractional oscillator. The bifurcation diagram construction algorithm was implemented not only in a sequential version but also in a parallel version, leveraging the computing power of the central processing unit (CPU). The algorithm automatically determines the number of CPU threads, and the user can select the required number for faster bifurcation diagram construction. In this article, we present bifurcation diagrams constructed depending on the characteristic time scale of $\theta$. It is shown that, depending on this scale and the orders of fractional derivatives, various oscillatory modes can arise, transitioning from one to another. This makes it possible to determine the ranges of $\theta$ parameter values within which a particular mode exists, which is important for solving specific applied problems.