The paper «Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients» has been published in Mathematics Journal by MDPI Publisher

The author is the Leading Researcher of the Laboratory of Physical Process Modeling of IKIR FEB RAS, Dr. Sci. (Phys.-Math.) Parovik Roman.

This article uses an approach based on the triad model–algorithm–program.

The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov–Caputo type.

The Adams–Bashforth–Multon numerical method from the predictor–corrector family of methods is selected as an algorithm for studying this system.

The ABMSelkovFracSim 1.0 software package acts as a program, in which a numerical algorithm with the ability to visualize the research results is implemented to build oscillograms and phase trajectories.

Examples of the ABMSelkovFracSim 1.0 software package operation for various values of the model parameters are given. It is shown that with an increase in the values of the parameter responsible for the characteristic time scale, regular and chaotic modes are observed.

Further in this work, bifurcation diagrams are constructed, which confirm this. Aperiodic modes are also detected and a singularity is revealed.

Full text of the paper is available at the link.

For references: Parovik, R. Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients. Mathematics 2025, 13, 372. https://doi.org/10.3390/math13030372