Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics

Larger, Laurent; Goedgebuer, J.-P.; Mérolla, Jean-Marc

doi:10.1109/3.663432

Cited by 53 publications

(17 citation statements)

References 18 publications

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“…The algorithm described in this section is not restricted either to noiseless numerical time series. As an illustration, we compute the reconstructed sub-LEλ 0 for time series recorded from an optoelectronic experimental setup, which can be modeled using the Ikeda delay system [32,33]. This optoelectronic system is properly described by Eq.…”

Section: Continuous Systemmentioning

confidence: 99%

Determining the sub-Lyapunov exponent of delay systems from time series

2015

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For delay systems the sign of the sub-Lyapunov exponent (sub-LE) determines key dynamical properties. This includes the properties of strong and weak chaos and of consistency. Here we present a robust algorithm based on reconstruction of the local linearized equations of motion, which allows for calculating the sub-LE from time series. The algorithm is inspired by a method introduced by Pyragas for a nondelayed drive-response scheme [K. Pyragas, Phys. Rev. E 56, 5183 (1997)]. In the presented extension to delay systems, the delayed feedback takes over the role of the drive, whereas the response of the low-dimensional node leads to the sub-Lyapunov exponent. Our method is based on a low-dimensional representation of the delay system. We introduce the basic algorithm for a discrete scalar map, extend the concept to scalar continuous delay systems, and give an outlook to the case of a full vector-state system, from which only a scalar observable is recorded.

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Section: Continuous Systemmentioning

confidence: 99%

Determining the sub-Lyapunov exponent of delay systems from time series

2015

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“…Considerable research has been conducted on the topics of chaotic resonators and chaotic oscillators (for instance, Reference [2,6,8,11,13,16,20,27,28,32,34,35,37,38,41,53,61,62]). However, few studies have considered the narrow-band response of a non-deterministic resonant system, as in the case of our research.…”

Section: Introductionmentioning

confidence: 99%

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Ueno

Fan

2012

Japan J. Indust. Appl. Math.

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This paper describes similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos, with particular emphasis on the geometric characteristics of trajectories reconstructed in m-dimensional phase space from measured scalar time series data with a time-delay coordinate system. In this study, the time series data of ship roll angle in irregular waves were analyzed as an example of the narrow-band response of a resonant system. These time series data were measured by one of the authors in Tokyo Bay. The similarities between the narrow-band response of a resonant system excited by random inputs and low-dimensional chaos are verified by numerical simulation data.

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“…Pockell cells or integrated optics Mach-Zehnder (MZ) modulator [3][4][5]) for the tuning of the intensity interference condition f [y]. In the same vein, our group in France developed various optoelectronic version of the Ikeda setup, while investigating a new application on chaos cryptography [6,7]. The setups are allowing for a highly nonlinear dynamics, thus leading to high complexity chaos, that is suspected to be well suited for the security of chaos based communications [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Optoelectronic delay dynamics: from optical chaos communication to high purity microwave oscillators

2007

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Nonlinear delay oscillators in optics have been first intensively studied in the context of chaos and nonlinear dynamics theory in the early 80s. Ten years later, they have been independently and nearly simultaneously explored in the context of two antagonistic applications: one is concerned by broadband spread spectrum optical chaos communications and the other dealt with ultra high spectral purity microwave oscillations. We report here on recent surprising results obtained while developing nonlinear dynamical stability analysis for each application, and considering the relevant quantitative differences between the two configurations of the same oscillator architectures. a e-mail:

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Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics

Cited by 53 publications

References 18 publications

Determining the sub-Lyapunov exponent of delay systems from time series

Determining the sub-Lyapunov exponent of delay systems from time series

Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas

Optoelectronic delay dynamics: from optical chaos communication to high purity microwave oscillators

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