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

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Chaos Theory and Applications
Volume:5 Issue:1
Alpha-Stable Autoregressive Modeling of Chua`s Circuit in the Presence of Heavy-Tailed Noise

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

Authors : Serpil YILMAZ, Deniz KUTLUAY

Pages : 3-10

Doi:10.51537/chaos.1162383

View : 35 | Download : 8

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :This study presents alpha-stable autoregressive insert ignore into journalissuearticles values(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.
Keywords : Alpha stable distribution, Chua, Autoregressive model, Yule Walker equation

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