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

Abstract

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.

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

“…The importance of additive noise in chaotic attractors is considered in (Argyris et al 1998). The effect of stochastic excitations which have asymmetric distributions on chaotic dynamics is analyzed in (Yilmaz et al 2018) by considering the generalized Chua's circuit driven by skew-Gaussian distributed noise. However, Gaussian distribution cannot be applied for modeling data across multiple application areas for which real-world data exhibit significant peaks.…”