- Chaos Theory and Applications
- Vol: 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 : 12 | Download : 7
Publication Date : 2023-03-31
Article Type : Research
Abstract :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.Keywords : Alpha-stable distribution, Chua, Autoregressive model, Yule-Walker equation