Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov

Abstract

The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benettin-Wolf algorithm. It is shown that the existence of chaotic regimes is possible. In particular, the spectrum of the maximum Lyapunov exponents of the order of the fractional derivative contains positive values, which indicates the presence of a chaotic regime. Phase trajectories were also constructed to confirm these results. It was also confirmed that the orders of fractional derivatives are responsible for dissipation in the system under consideration.