Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients

Roman Parovik ()
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Roman Parovik: Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034 Paratunka, Russia

Mathematics, 2025, vol. 13, issue 3, 1-10

Abstract: 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.

Keywords: fractional Selkov dynamic system; fractional derivative of variable order; Adams–Bashforth–Moulton method; software package ABMSelkovFracSim 1.0; phase trajectories; oscillograms; bifurcation diagrams; Python (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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