Studies of the fractional Selkov dynamical system to describe the self-oscillatory regime of microseisms

   The paper describes a non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena. 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.

   Parovik R. I. Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms. Mathematics 2022, 10(22), 4208; DOI:10.3390/math10224208, https://doi.org/10.3390/math10224208