Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms

Roman Ivanovich Parovik ()
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Roman Ivanovich Parovik: Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 7, Mirnaya St., Yelizovsky District, Paratunka 684034, Russia

Mathematics, 2022, vol. 10, issue 22, 1-14

Abstract: A non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena is proposed. This system is a generalization of the previously known Selkov system, which has self-oscillatory modes and is used in biology to describe glycolytic vibrations of the substrate and product. The Selkov fractional dynamical system takes into account the influence of heredity and is described using derivative fractional orders. The article investigates the Selkov fractional dynamic model using the Adams–Bashforth–Moulton numerical method, constructs oscillograms and phase trajectories, and studies the equilibrium points. Based on the spectra of the maximum Lyapunov exponents, it is shown that in the fractional dynamic model there can be relaxation and damped oscillations.

Keywords: fractional Selkov dynamic system; Adams–Bashforth–Moulton method; microseisms; equilibrium points; self-oscillations; phase trajectories; oscillograms; spectrum of maximum Lyapunov exponents (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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