Publisher’s Note: Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization [Phys. Rev. E<b>68</b>, 066208 (2003)]

Schlesner, J.; Amann, Andreas; Janson, Natalia B.; Just, Wolfram; Schöll, Eckehard

doi:10.1103/physreve.69.029901

Cited by 13 publications

(19 citation statements)

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“…An extension to multiple time-delays (extended time-delay autosynchronization) has been proposed by Socolar et al [4], and analytical insight into those schemes has been gained by several theoretical studies [5][6][7][8]. Such self-stabilizing feedback control schemes (time-delay autosynchronization) with different couplings of the control force have been applied to various classes of deterministic ordinary and partial differential equations, modelling, e.g., semiconductor oscillators [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Controlling Stochastic Oscillations Close to a Hopf Bifurcation by Time-Delayed Feedback

et al. 2005

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We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.

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Section: Introductionmentioning

confidence: 99%

Controlling Stochastic Oscillations Close to a Hopf Bifurcation by Time-Delayed Feedback

et al. 2005

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“…In [9] it has been predicted analytically by a linear expansion that control is realized only in a finite range of the values of K: at the lower control boundary the limit cycle should undergo a period-doubling bifurcation, and at the upper boundary a Hopf bifurcation generating a stable or an unstable torus from a limit cycle (Neimark-Sacker bifurcation). Although the linear expansion becomes exact only for a special coupling of the control force in the form of a unity matrix (diagonal coupling), this general bifurcation behavior has been numerically verified in a large number of diverse delayed feedback control systems including spatially extended reaction-diffusion systems [23][24][25]. The feedback scheme (2) we use here is non-diagonal, but in qualitative agreement with [9], at K ≈ 0.24 the stable limit cycle undergoes a period-doubling bifurcation, and at K ≈ 2.3 a Neimark-Sacker bifurcation.…”

Section: Survey Of the Bifurcation Diagrammentioning

confidence: 99%

Delayed feedback control of chaos: Bifurcation analysis

2005

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We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rössler system. We reveal the general bifurcation diagram in the parameter plane of time delay τ and feedback strength K which allows one to explain the phenomena that have been discovered in some previous works. We show that the bifurcation diagram has essentially a multi-leaf structure that constitutes multistability: the larger the τ , the larger the number of attractors that can coexist in the phase space. Feedback induces a large variety of regimes non-existent in the original system, among them tori and chaotic attractors born from them. Finally, we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system.

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“…where α is the cutoff frequency and K the control amplitude [10]. Since both voltage and total current density are externally accessible global variables, such a control scheme is easy to implement experimentally.…”

Section: Ns) T Marks the Pulse Duration In (A) Dashed (Red) Curves mentioning

confidence: 99%

Control of noise‐induced spatiotemporal patterns in superlattices

Hizanidis

Schöll

2008

Phys. Status Solidi (c)

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We investigate a semiconductor superlattice exhibiting complex dynamics of electron accumulation and depletion fronts (travelling field domains) in the presence of noise and control. In the uncontrolled system noise is able to induce electron charge front motion through the device when the system is prepared near a global bifurcation which yields it highly sensitive to fluctuations. The associated current density oscillations exhibit a maximum of coherence at an optimal noise intensity, a phenomenon known as coherence resonance. We show how control in the form of a time‐delayed feedback signal affects the noise‐induced dynamics. We observe that control induces a limit cycle in a wide range of the control parameter space and therefore destroys the effect of coherence resonance. For low noise intensity, time‐delayed feedback control enhances the regularity (coherence) of the noisy oscillations considerably. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Publisher’s Note: Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization [Phys. Rev. E68, 066208 (2003)]

Cited by 13 publications

References 0 publications

Controlling Stochastic Oscillations Close to a Hopf Bifurcation by Time-Delayed Feedback

Controlling Stochastic Oscillations Close to a Hopf Bifurcation by Time-Delayed Feedback

Delayed feedback control of chaos: Bifurcation analysis

Control of noise‐induced spatiotemporal patterns in superlattices

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