Delayed feedback control for the system with hyperbolic attractor

Белякин, С.Т.; Джаноев, А.Р.; Лоскутов, А.Ю.

Авторы: Белякин С.Т., Джаноев А.Р., Лоскутов А.Ю.
Сборник: 20th IEEE-Workshop Nonlinear Dynamics of Electronic Systems - NDES 2012
Серия: 20
Том: 1
Тезисы
Год издания: 2012
Место издания: Nonlinear Dynamics of Electronic Systems VDE (Verband der Elektrotechnik - Elektronik - Informationstechnik e. V. ) in Germany
Первая страница: 18
Последняя страница: 18
Аннотация: Delayed feedback control for the system with hyperbolic attractor Sergey Belyakin, Arsen Dzhanoev, Alexander Loskutov M. V. Lomonosov Moscow State University, Moscow, Russia; bst@newmail.ru University of Potsdam, Potsdam, Germany; For a long time it was a common opinion that hyperbolic attractors are artificial mathematical The unique feature of this conference is to bring together all theoretical aspects of nonlinear sciences of electrical engineering, physics and mathematics, as well as related applications. Nonlinear oscillations, synchronization, chaotic behavior, neural networks and complex systems together with power electronics, biomedical systems and neurocomputing are a few topical examples for the need of expertise in the wide field of nonlinear sciences. Additionally, several invited talks are given with respect to the 100th anniversary of the death of Henri Poincaré, who was one of the founders of nonlinear sciences in the second half of the nineteenth century. constructions [1]. However, in the recent papers [2, 3] there were proposed physically realizable systems that possess, in their phase space, the set with features that are very similar to hyperbolic type of attractors. As is known, invariant sets are called hyperbolic attractors of the dynamical system if they are closed, topologically transitive subsets, and every their trajectory possesses uniform hyperbolicity. Very familiar types of the hyperbolic attractors are Smale-Williams’ solenoid and Plykin’s attractor. Further, it is well known that chaotic systems are very sensitive to the external perturbations. This property is used for controlling nonlinear systems and chaos suppression. Thus, an important question arises: Is it possible to suppress chaos in systems with hyperbolic attractors because these attractors are structurally stable subsets? In the present contribution we study the possibility of stabilization of chaotic oscillations in systems with the Smale-Williams hyperbolic attractors by means of the Pyragas method with a delay [4]. It is shown that by means of external perturbation the dynamical system could be controllable: the hyperbolic attractor degenerates into a periodic one. [1] A. Loskutov. Physics–Uspekhi 53 1255 (2010). [2] S.P. Kuznetsov. Phys. Rev. Lett. 95 144101 (2005). [3] S.P. Kuznetsov and A. Pikovsky. Physica D 232 87 (2007). [4] K. Pyragas. Phys. Lett. A 170 421 (1992).
Добавил в систему: Белякин Сергей Тихонович

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Delayed feedback control for the system with hyperbolic attractorтезисы доклада

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