Extended resonant feedback technique for controlling unstable periodic orbits of chaotic system |
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Authors: | Ar nas Tama evi
ius, Elena Tama evi
i t , Tatjana Pyragien , Gytis Mykolaitis,Skaidra Bumelien |
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Affiliation: | aPlasma Phenomena and Chaos laboratory, Semiconductor Physics Institute, A. Goštauto 11, Vilnius LT-01108, Lithuania;bDepartment of General Physics and Spectroscopy, Faculty of Physics, Vilnius University, Saulėtekio 9, Vilnius LT-10222, Lithuania |
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Abstract: | An improvement of the recently described resonant chaos control method is suggested. Negative feedback loop containing a notch-rejection filter, tuned to the main harmonic of the unstable periodic orbit, is supplemented with a set of notch filters tuned to the higher harmonics. The extended method is applied to an electrical circuit representing the Duffing–Holmes type non-autonomous two-well chaotic oscillator. Stabilization of the period-1 orbit is achieved with very small control force. The residual control signal is about 1% compared to the main variable. Mathematical model based on a two-well piecewise parabolic potential is presented and numerical simulation is performed. Numerical results are confirmed by hardware experiments. |
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Keywords: | Non-linear dynamics Low-dimensional chaos Control of chaos |
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