Application of a modified 0-1 test algorithm for the analysis of chaotic modes in a fractional duffing oscillator

The article studies the modes of the fractional Duffing oscillator with the Riemann-Liouville derivative of fractional variable order. The research tool is a modified Test 0-1 algorithm, which allows constructing bifurcation diagrams characterizing the chaotic or regular behavior of a dynamic system. The input of the algorithm is the calculated values of the Duffing fractional oscillator bias obtained using a numerical algorithm, from which local extrema are preliminarily removed in order to reduce the influence of the resampling effect. Using the MATLAB computer system, in which the Test 0-1 algorithm was implemented, bifurcation diagrams were constructed depending on the values of the friction coefficient and the orders of fractional derivatives. The presence of both regular and chaotic modes in the Duffing fractional oscillator is shown, which is also confirmed by oscillograms and phase trajectories.