Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback

Hramov, Alexander E.; Короновский, А. А.; Rempen, I.S.

doi:10.1063/1.2168394

Cited by 23 publications

(17 citation statements)

References 62 publications

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“…2,3 For example, the knowledge of several largest Lyapunov exponents can be used for chaos control through "unstable periodic orbit stabilization" 3,4,62,63 or for characterization of different types of chaos synchronization [64][65][66] in plasma or electronic devices.…”

Section: Discussionmentioning

confidence: 99%

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Lyapunov stability of charge transport in miniband semiconductor superlattices

et al. 2013

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Section: Discussionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7] Such systems can demonstrate a variety of dynamical behavior, including deterministic chaos. 5,[8][9][10] However, stability analysis (even numerical) of the systems away from the equilibrium still remains a nontrivial problem.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov stability of charge transport in miniband semiconductor superlattices

et al. 2013

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“…Recently, the successful attempt to compute the highest Lyapunov exponent taking into account the core features of the spatially extended systems has been made for plasma system models [5,12]. In the present work we develop the technique of the spectrum of the spatial Lyapunov exponents (SLEs) calculation for the distributed beam-plasma systems and electron-wave devices.…”

Section: Introductionmentioning

confidence: 99%

Computation of the spectrum of spatial Lyapunov exponents for the spatially extended beam-plasma systems and electron-wave devices

et al. 2012

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The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamical systems a number of the numerical technics have been developed to obtain the spectrum of Lyapunov exponents for the complex temporal behavior of the systems with a few degree of freedom. Unfortunately, these methods can not apply directly to analysis of complex spatio-temporal dynamics in plasma devices which are characterized by the infinite phase space, since they are the spatially extended active media. In the present paper we propose the method for the calculation of the spectrum of the spatial Lyapunov exponents (SLEs) for the spatially extended beam-plasma systems. The calculation technique is applied to the analysis of chaotic spatio-temporal oscillations in three different beam-plasma model: (1) simple plasma Pierce diode, (2) coupled Pierce diodes, and (3) electron-wave system with backward electromagnetic wave. We find an excellent agreement between the system dynamics and the behavior of the spectrum of the spatial Lyapunov exponents. Along with the proposed method, the possible problems of SLEs calculation are also discussed. It is shown that for the wide class of the spatially extended systems the set of quantities included in the system state for SLEs calculation can be reduced using the appropriate feature of the plasma systems. PACS numbers: 05.45.-a, 05.10.-a Keywords: spectrum of Lyapunov exponents, spatially extended systems, beam plasma systems, electron wave media, Pierce diode, transverse field backward wave oscillator, reference system state.

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“…It is important to notice that the Pierce diode is a well studied model of beam-plasma systems, demonstrating complex chaotic oscillations. In particular, the routes to spatial chaos, 24,25 pattern formation, 31 controlling chaos, 26,[32][33][34] and synchronization 35,36 have been studied in great details.…”

Section: Introductionmentioning

confidence: 99%

Synchronization in networks of spatially extended systems

Filatova

Hramov

Короновский

et al. 2008

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Synchronization processes in networks of spatially extended dynamical systems are analytically and numerically studied. We focus on the relevant case of networks whose elements (or nodes) are spatially extended dynamical systems, with the nodes being connected with each other by scalar signals. The stability of the synchronous spatio-temporal state for a generic network is analytically assessed by means of an extension of the master stability function approach. We find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations. The efficiency and reliability of this method is illustrated numerically with networks of beam-plasma chaotic systems (Pierce diodes). We discuss also how the revealed regularities are expected to take place in other relevant physical and biological circumstances.

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Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback

Cited by 23 publications

References 62 publications

Lyapunov stability of charge transport in miniband semiconductor superlattices

Lyapunov stability of charge transport in miniband semiconductor superlattices

Computation of the spectrum of spatial Lyapunov exponents for the spatially extended beam-plasma systems and electron-wave devices

Synchronization in networks of spatially extended systems

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