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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Analysis of Discontinuous Bifurcations in Nonsmooth Dynamical Systems
Alexander P. Ivanov Moscow Institute of Physics and Technology, Inststitutskii per. 9, Dolgoprudnyi, 141700 Russia
Аннотация:
Dynamical systems with discontinuous right-hand sides are considered. It is well known that the trajectories of such systems are nonsmooth and the fundamental solution matrix is discontinuous. This implies the presence of the so-called discontinuous bifurcations, resulting in a discontinuous change in the multipliers. A method of stepwise smoothing is proposed allowing the reduction of discontinuous bifurcations to a sequence of typical bifurcations: saddlenode, period doubling and Hopf bifurcations. The results obtained are applied to the analysis of the well-known dry friction oscillator, which serves as a popular model for the description of self-excited frictional oscillations of a braking system. Numerical techniques used in previous investigations of this model did not allow general conclusions to be drawn as to the presence of self-excited oscillations. The new method makes it possible to carry out a complete qualitative investigation of possible types of discontinuous bifurcations in this system and to point out the regions of parameters which correspond to stable periodic regimes.
Ключевые слова:
nonsmooth dynamical systems, discontinuous bifurcations, oscillators with dry friction.
Поступила в редакцию: 14.03.2012 Принята в печать: 07.05.2012
Образец цитирования:
Alexander P. Ivanov, “Analysis of Discontinuous Bifurcations in Nonsmooth Dynamical Systems”, Regul. Chaotic Dyn., 17:3-4 (2012), 293–306
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd403 https://www.mathnet.ru/rus/rcd/v17/i3/p293
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