Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model

Weiß, C. O.; Vilaseca, R.; Abraham, N. B.; Corbalán, R.; Roldán, Eugenio; Valcárcel, Germán J. de; Pujol, Jaume; Hübner, U.; Tang, Dingyuan

doi:10.1007/bf01082041

Cited by 27 publications

(5 citation statements)

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“…Chaotic lasers too have been widely reported. For example, Weiss et al reported an exact correspondence between the far-infrared megaherz ammonia laser and a chaotic Lorenz-like system [22], [23], and more recently, Van Wiggeren et al demonstrated communication with chaotic lasers [16]. In short, such wide ranging experiments with chaotic systems suggests that the chaotic computing schemes discussed in this brief will be feasible.…”

Section: Methodsmentioning

confidence: 90%

Chaos computing: implementation of fundamental logical gates by chaotic elements

Munakata

Sinha

Ditto

2002

IEEE Trans. Circuits Syst. I

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Abstract-Basic principles of implementing the most fundamental computing functions by chaotic elements are described. They provide a theoretical foundation of computer architecture based on a totally new principle other than silicon chips. The fundamental functions are: the logical AND, OR, NOT, XOR, and NAND operations (gates) and bit-by-bit arithmetic operations. Each of the logical operations is realized by employing a single chaotic element. Computer memory can be constructed by combining logical gates. With these fundamental ingredients in hand, it is conceivable to build a simple, fast, yet cost effective, general-purpose computing device. Chaos computing may also lead to dynamic architecture, where the hardware design itself evolves during the course of computation. The basic ideas are explained by employing a one-dimensional model, specifically the logistic map.Index Terms-Chaos computing, new computing paradigm, one-dimensional (1-D) chaotic systems.

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Section: Methodsmentioning

confidence: 90%

Chaos computing: implementation of fundamental logical gates by chaotic elements

Munakata

Sinha

Ditto

2002

IEEE Trans. Circuits Syst. I

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“…The basic idea is to study the optical field composed of a reference and a source field. This optical technique has allowed the confirmation of predictions from the Lorenz model, which describes to a good degree the dynamics of the N H 3 -laser [25]. Similarly, heterodyne optical techniques have been used to study optical fields in two-dimensional light sources [18], which are precisely the geometries that support stable choreographies.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Within the context of nonlinear optics, several predictions of the DNLSE have been found experimentally in the last two decades [17], such as the formation of discrete solitons in waveguide arrays. The use of suitable optical techniques, known as laser heterodyne measurements, to detect the field intensity and the phase [25,18], may open the door to experimental observation of stable choreographic solutions.…”

Section: Introductionmentioning

confidence: 99%

Choreographies in the discrete nonlinear Schrödinger equations

Calleja

Doedel

García-Azpeitia

et al. 2018

Eur. Phys. J. Spec. Top.

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We study periodic solutions of the discrete nonlinear Schrödinger equation (DNLSE) that bifurcate from a symmetric polygonal relative equilibrium containing n sites. With specialized numerical continuation techniques and a varying physically relevant parameter we can locate interesting orbits, including infinitely many choreographies. Many of the orbits that correspond to choreographies are stable, as indicated by Floquet multipliers that are extracted as part of the numerical continuation scheme, and as verified a posteriori by simple numerical integration. We discuss the physical relevance and the implications of our results.

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“…Therefore, in order to make all variables accessible, we use the equivalent one-dimensional third order system (13). As input variables for the multiple nonparametric regression problem (9) we use…”

Section: Parametric Modelling Imentioning

confidence: 99%

“…The validity of a specific model can be evaluated by comparing properties of simulated time series with the measured one (9). This approach faces a dilemma.…”

Section: Introductionmentioning

confidence: 99%

Parametric, nonparametric and parametric modelling of a chaotic circuit time series

Timmer¹,

Rust²,

Horbelt³

et al. 2000

Physics Letters A

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The determination of a differential equation underlying a measured time series is a frequently arising task in nonlinear time series analysis. In the validation of a proposed model one often faces the dilemma that it is hard to decide whether possible discrepancies between the time series and model output are caused by an inappropriate model or by bad estimates of parameters in a correct type of model, or both. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a chaotic circuit where we obtain an extremely accurate reconstruction of the observed attractor. PACS: 05.45.Tp,

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Models, predictions, and experimental measurements of far-infrared NH3-laser dynamics and comparisons with the Lorenz-Haken model

Cited by 27 publications

References 50 publications

Chaos computing: implementation of fundamental logical gates by chaotic elements

Chaos computing: implementation of fundamental logical gates by chaotic elements

Choreographies in the discrete nonlinear Schrödinger equations

Parametric, nonparametric and parametric modelling of a chaotic circuit time series

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