Duffing spatial dynamics induced in a double phase-conjugated resonator

Dignowity, D; Wilson, Mario; Rangel-Fonseca, Piero; Aboites, Vicente

doi:10.1088/1054-660x/23/7/075002

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…These include a higher‐order autoregressive model (AR4) and a nonlinear threshold autoregressive model (TAR), which were investigated previously by Cryer and Chan (), Galelli et al (), and Sharma and Mehrotra (). Duffing system (Dignowity et al, ; Duffing, ) is another example of a dynamical system that exhibits chaotic behavior. In all synthetic experiments, our proposed method exhibits superior accuracy than the reference model using nontransformed predictors in terms of RMSE, correlation, and standard deviation.…”

Section: Application To a Dynamic Examplementioning

confidence: 99%

Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling

Jiang

Sharma

2020

Water Resources Research

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Predicting future surpluses or shortages of water is a long‐standing problem having considerable ramifications to water management across the world. Any prediction model for a natural system such as one that estimates water surpluses or shortages requires a two‐step approach. These are the following: first, identify and select meaningful predictor variables from a large number of potential predictors and second, formulate an accurate, efficient, and robust predictive model between selected predictors and the response. Recognizing that the timescales at which a response may operate is usually different from that of the predictors being identified, we introduce here a wavelet‐based unique variance transformation to each of the multiple predictor variables in the system which ensures an improved regression relationship to the modeled response. All existing methods assume no change in predictors even if they characterize variability at markedly different timescales, a deficiency that is addressed using the variance‐transformed predictor which can explain maximal information in an associated response. Using this unique variance transformation, additional predictor variables can be selected by assessing their ability to characterize residual information in the response that accounts for the effect of preidentified predictors. We demonstrate the utility of the wavelet‐based method using synthetically generated data sets from known linear and nonlinear systems with parametric and nonparametric predictive models. Applications to a dynamic system and a real‐world example to downscale a drought indicator over the Sydney region confirm its utility in an applied setting.

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Section: Application To a Dynamic Examplementioning

confidence: 99%

Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling

Jiang

Sharma

2020

Water Resources Research

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“…As shown, the behavior of a beam may be obtained by making an arbitrary well-defined chaotic map [10,11,12]. Particularly, the Henón [14], Bogdanov [15], Ikeda [16], Duffing [17,18], Standard [19] and Tinkerbell maps [20,21] were employed, among others. Here, for the first time to the best of our knowledge, a PC laser ring cavity is designed to produce Van del Pol beams within certain welldefined parameters.…”

Section: Introductionmentioning

confidence: 99%

Laser cavity with a Van der Pol dynamics

et al. 2021

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In this article, a beam within a ring phase conjugated laser is described by means of a Van der Pol bidimensional dynamic map using an ABCD matrix approach. Explicit expressions for the intracavity chaos-generating matrix elements were obtained; furthermore, computer calculations for different values of Van der Pol map’s parameters were made. The rich dynamic behavior displays periodicity when the parameter ¹ (which determines the non-inearity term) takes values around zero. These results were observed in phase diagrams and in diagrams of the optical thickness of the intracavity element.

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“…This kind of map has been successfully applied before to the description of laser beams within optical resonators. This treatment has been explored for several other maps, obtaining several chaos-generating intracavity elements that are based on the dynamical behavior from widely diverse maps, such as the Ikeda map [7], Standard map [8], Tinkerbell map [9][10][11], Duffing map [11,12], logistic map [13] and the Henón map [11,14]. Throughout this article the Bogdanov Map will be used to describe a ring-phase conjugated resonator, while the resultant iterative matrix system is analyzed.…”

Section: Introductionmentioning

confidence: 99%

Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

Aboites

Liceaga

Jaimes-Reátegui

et al. 2019

Entropy

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In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element.

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Duffing spatial dynamics induced in a double phase-conjugated resonator

Cited by 6 publications

References 14 publications

Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling

Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling

Laser cavity with a Van der Pol dynamics

Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

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