Identifying and Modeling Delay Feedback Systems

Hegger, Rainer; Bünner, M. J.; Kantz, Holger; Giaquinta, A.

doi:10.1103/physrevlett.81.558

Cited by 199 publications

(116 citation statements)

References 15 publications

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“…Recent studies on prediction address system identification and model development [7], as well as the use of anticipated synchronization between coupled identical systems [8]. In this work, we demonstrate that synchronization of a numerical model to an experimentally measured waveform allows us to both forecast the future dynamics of a high-dimensional system and estimate the local maximum Lyapunov exponent and its distribution.…”

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confidence: 74%

“…In networked sensor arrays designed to detect spatiotemporal disturbances, prediction methods could enable efficient acquisition and incorporation of data from multiple sensors [5]. In biomedical treatment, prediction models could lead to improved strategies for adjusting drug dosage and delivery or physiological control [6].Recent studies on prediction address system identification and model development [7], as well as the use of anticipated synchronization between coupled identical systems [8]. In this work, we demonstrate that synchronization of a numerical model to an experimentally measured waveform allows us to both forecast the future dynamics of a high-dimensional system and estimate the local maximum Lyapunov exponent and its distribution.…”

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confidence: 99%

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Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics

et al. 2008

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We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization of a numerical model to experimental measurements provides a new way to assimilate data and forecast the future of this time-delayed high-dimensional system. For this system, which has a feedback time delay of 22 ns, we show that one can predict the time series for up to several delay periods, when the dynamics is about 15 dimensional. The question of how to predict the future of a dynamical system with time delay is of interest in many applications [1][2]. In chaotic encrypted communication systems, the predictability is related to how difficult it would be for an eavesdropper to intercept a message. A better understanding of predictability in these systems could guide the development of new strategies to improve security, such as periodically changing the system parameters or protocols to avoid interception [3]. Prediction and anticipation are thought to underlie the process of image recognition and motion tracking in the retina [4]. In networked sensor arrays designed to detect spatiotemporal disturbances, prediction methods could enable efficient acquisition and incorporation of data from multiple sensors [5]. In biomedical treatment, prediction models could lead to improved strategies for adjusting drug dosage and delivery or physiological control [6].Recent studies on prediction address system identification and model development [7], as well as the use of anticipated synchronization between coupled identical systems [8]. In this work, we demonstrate that synchronization of a numerical model to an experimentally measured waveform allows us to both forecast the future dynamics of a high-dimensional system and estimate the local maximum Lyapunov exponent and its distribution. The inverse of the maximum Lyapunov exponent defines the prediction horizon -the time over which the system behavior can be forecast.The optoelectronic system studied is shown in Figure 1. A similar system was used by Argyris et al. as a transmitter and receiver for a high-speed chaotic communication 1

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Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics

et al. 2008

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“…As it is stated in ref. [17] the Kaplan-Yorke dimension of this system is D KY ∼ 13.5, which, according to the Kaplan-Yorke conjecture, D KY = D 1 , for a typical attractor. We have made a standard reconstruction analysis over time series of up to 16384 data points.…”

Section: A Generalized Mackey-glass Systemmentioning

confidence: 99%

“…In order to investigate how our algorithm work on high dimensional systems, we use a generalization of the Mackey-Glass (MG) equation [17], a delayed feedback system,ẋ…”

Section: A Generalized Mackey-glass Systemmentioning

confidence: 99%

Detecting determinism in high-dimensional chaotic systems

2001

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A method based upon the statistical evaluation of the differentiability of the measure along the trajectory is used to identify determinism in high dimensional systems. The results show that the method is suitable for discriminating stochastic from deterministic systems even if the dimension of the latter is as high as 13. The method is shown to succeed in identifying determinism in electro-encephalogram signals simulated by means of a high dimensional system.

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“…Two widely applied techniques are the autocorrelation function (ACF) and the delay mutual information (DMI) [14] . Other techniques include the phase information [15] , the minimal forecast error [16] , the filling factor analysis [17] , the permutation-information theory [18] , and the extrema interval analysis [19] . In 2010, we found that the TD signature could be identified through observing the RF power spectral and observing its fine structure [20] .…”

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Method to identify time delay of chaotic semiconductor laser with optical feedback

Guo¹,

Yuan²,

Wang³

2012

中国光学快报

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We propose a power spectrum analysis method to directly identify the time delay of a chaotic semiconductor laser with optical feedback. By measuring the radio frequency (RF) power spectrum of the chaotic laser and performing an inverse Fourier transform, we can easily unveil all the time delay signatures, regardless of whether the chaotic output is induced by single or multiple feedback. This method successfully retrieves the two time delay signatures from the power spectrum of a semiconductor laser with double-cavity feedback.OCIS codes: 190.3100, 140.5960. doi: 10.3788/COL201210.061901. Optical chaos has attracted considerable attention in recent years due to its great applications in various fields, such as chaos-based communication encryption systems [1] , chaotic lidars [2] , fast random bit sequences generators (RNGs) [3] , and chaotic optical time-domain reflectometry [4] . Through perturbing a semiconductor laser (SL) with optical injection, optical feedback, or optoelectronic feedback, the laser can be driven into broadband chaotic output [5] . Among the mentioned methods, the semiconductor laser with optical feedback (SL-OFB) may be the most common applied chaotic sources due to its unique virtues, such as simple configuration, small size, feasible controllability, and rich chaotic dynamics.Nevertheless, the output of SL-OFB usually has periodic intensity fluctuations. These fluctuations are nearly identically repeated at the photon round-trip time in the external cavity, and are widely called the time delay (TD) signature. The TD signature seriously affects the performance of chaotic system in some applications. For example, the TD signature provides the clue to break the chaos-based secure communication and can deteriorate the randomness of RNGs based on SL-OFB. Some scenarios have been proposed to conceal the TD signature of SL-OFB. Typical scenarios are to generate high-dimensional chaos [6] , to modulate the delay time [7,8] , and to use multiple feedback [9,10] . Recently, Wu et al. experimentally showed that the TD signatures can be suppressed in two limits when double external cavities are used; one is that the two external cavities have roughly equal lengths, and the other is that one cavity length is approximately half of the other [11] . Rontani et al. proposed that TD signature identification would be impossible when the TD is close to the relaxation period of the laser operating with weak feedback [12] . Their theory was demonstrated experimentally in 2010 [13] . In contrast, several techniques for extracting the TD signature also exist; however, usually, their observables are the recorded chaotic time series. Two widely applied techniques are the autocorrelation function (ACF) and the delay mutual information (DMI) [14] . Other techniques include the phase information [15] , the minimal forecast error [16] , the filling factor analysis [17] , the permutation-information theory [18] , and the extrema interval analysis [19] . In 2010, we found that the TD signature could be identified t...

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Identifying and Modeling Delay Feedback Systems

Cited by 199 publications

References 15 publications

Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics

Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics

Detecting determinism in high-dimensional chaotic systems

Method to identify time delay of chaotic semiconductor laser with optical feedback

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