Geodesic
Implementation of the modified Test 0-1 algorithm for the analysis of chaotic modes of the fractional Duffing oscillator
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 44 (2023) no. 3, pp. 67-85

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The work carried out a study of chaotic and regular modes of a fractional Duffing oscillator using the Test 0-1 algorithm. The fractional Duffing oscillator is described by a nonlinear differential equation with the Riemann-Liouville derivative of a fractional variable order. Using an explicit numerical finite difference scheme, a numerical solution to the model was obtained, which is fed to the input of the Test 0-1 algorithm after the thinning procedure – identifying local extrema. Next, using the Matlab package, the Test 0-1 algorithm is implemented and the simulation results are visualized. Bifurcation diagrams are constructed for the correlation coefficient, taking into account the values of the orders of the fractional derivative, and oscillograms and phase trajectories are constructed. It is shown that the Test 0-1 algorithm works correctly with the appropriate selection of the sampling step.
Keywords: Test 0-1, model, Duffing oscillator, Riemann-Liouville fractional derivative, standard deviation, correlation, bifurcation diagram. 
@article{VKAM_2023_44_3_a5,
     author = {R. I. Parovik},
     title = {Implementation of the modified {Test} 0-1 algorithm for the analysis of chaotic modes of the fractional {Duffing} oscillator},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {67--85},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2023_44_3_a5/}
}
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R. I. Parovik. Implementation of the modified Test 0-1 algorithm for the analysis of chaotic modes of the fractional Duffing oscillator. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 44 (2023) no. 3, pp. 67-85. http://geodesic.mathdoc.fr/item/VKAM_2023_44_3_a5/