Bayesian Stable Mixture Model of State Densities of Generalized Chua's Circuit

Savacı, F. Acar; Yilmaz, Serpil

doi:10.1142/s0218127415500388

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…Chua's circuit is a type of simple non-linear electronic circuit design [34,35], as shown in Figure 4. It is formed by four linear components, the inductor L, resistor R, capacitor According to Kirchhoff's Law, Chua's circuit status equation is shown as Equation (1).…”

Section: Chua's Circuitmentioning

confidence: 99%

Soil Salinization Level Monitoring and Classifying by Mixed Chaotic Systems

Tian

Yau

et al. 2021

Remote Sensing

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Soil salinization process is a complex non-linear dynamic evolution. To classify a system with this type of non-linear characteristic, this study proposed a mixed master/slave chaotic system based on Chua’s circuit and a fractional-order Chen-Lee chaotic system to classify soil salinization level. The subject is the soil in Xinjiang with different levels of human interference. A fractional-order Chen-Lee chaotic system was constructed, and the spectral signal processed by the Chua’s non-linear circuit was substituted into the master/slave chaotic system. The chaotic dynamic errors with different fractional orders were calculated. The comparative analysis showed that 0.1-order has the largest chaotic dynamic error change, which produced two distinct and divergent results. Thus, this study converted the chaotic dynamic errors of fractional 0.1-order into chaotic attractors to build an extension matter-element model. Finally, we compared the soil salt contents (SSC) from the laboratory chemical analysis with the results of the extension theory classification. The comparison showed that the combination of fractional order mixed master/slave chaotic system and extension theory has high classification accuracy for soil salinization level. The results of this system match the result of the chemical analysis. The classification accuracy of the calibration set data was 100%, and the classification accuracy of the validation set data was 90%. This method is the first use of the mixed master/slave chaotic system in this field and can satisfy certain soil salinization monitoring needs as well as promote the application of the chaotic system in soil salinization monitoring.

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Section: Chua's Circuitmentioning

confidence: 99%

Soil Salinization Level Monitoring and Classifying by Mixed Chaotic Systems

Tian

Yau

et al. 2021

Remote Sensing

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“…The normalized histograms can also be modeled by the¯nite mixture of -stable (FMS) distributions presented in [34]. Qualitative changes of histograms with respect to the critical noise intensity Ã are shown in Figs.…”

Section: P-bifurcation Of 7-scroll Attractormentioning

confidence: 99%

Stochastic Bifurcation in Generalized Chua’s Circuit Driven by Skew-Normal Distributed Noise

2018

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In this study, the stochastic phenomenological bifurcations (P-bifurcations) of generalized Chua’s circuit (GCC) driven by skew-normal distributed noise have been investigated by numerically obtaining the stationary distributions of the stochastic responses. The noise intensity and/or skewness parameters of skew-normal distributed noise have been chosen as the bifurcation parameters to change the structure of the stochastic attractor. While the number of breakpoints in the piecewise-linear characteristics of the GCC are fixed, it has been observed that the number of scrolls have been changed by tuning the noise intensity and the skewness parameter of the skew-normal distributed noise.

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“…Some examples that might have heavy-tailed behavior include tracking highly maneuvering objects (Gan and Godsill 2020;Gan et al 2021), interference in IoT networks (Clavier et al 2021), financial data (McCulloch 1996Maleki et al 2020;Janczura et al 2011;Wesselhöfft 2021), chaotic systems (Savaci and Yilmaz 2015;Contreras-Reyes 2021), frequency fluctuations in the power grid (Schäfer et al 2018;Anvari et al 2020), the dose distributions for proton breast treatment (Van den Heuvel et al 2015), proton pencil beams for cancer therapy (Van den Heuvel et al 2018), climate dynamics (Ditlevsen 1999;Broszkiewicz-Suwaj and Wyłoma ńska 2021). Therefore, alpha-stable (α-stable) distributions are more suitable for modeling such impulsive behavior (Nolan 2003).…”

Section: Introductionmentioning

confidence: 99%

Alpha-Stable Autoregressive Modeling of Chua's Circuit in the Presence of Heavy-Tailed Noise

Yilmaz

KUTLUAY²

2023

Chaos Theory and Applications

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This study presents alpha-stable autoregressive (AR) modeling of the dynamics of Chua's circuit in the presence of heavy-tailed noise. The parameters of the AR time series are estimated using the covariation-based Yule-Walker method, and the parameters of alpha-stable distributed residuals are calculated using the regression type method. Visual depictions of the calculated parameters of the AR model and alpha-stable distributions of residuals are presented. The medians of the estimated parameters of the AR model and alpha-stable distributions parameters of residuals are presented for heavy-tailed noise with various stability index parameters. Thus, the impulsive behavior of Chua's circuit can be modeled as alpha-stable AR time series, and the model can provide an alternative approach to describe the chaotic systems driven by heavy-tailed noise.

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Bayesian Stable Mixture Model of State Densities of Generalized Chua's Circuit

Cited by 4 publications

References 29 publications

Soil Salinization Level Monitoring and Classifying by Mixed Chaotic Systems

Soil Salinization Level Monitoring and Classifying by Mixed Chaotic Systems

Stochastic Bifurcation in Generalized Chua’s Circuit Driven by Skew-Normal Distributed Noise

Alpha-Stable Autoregressive Modeling of Chua's Circuit in the Presence of Heavy-Tailed Noise

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