Harmonic Balance Analysis of the Generalized Chua's Circuit

Abstract

READS 502 authors: Some of the authors of this publication are also working on these related projects: International Journal of Bifurcation and Chaos, Vol. 16, No. 8 (2006) In this paper, the harmonic balance analysis of Generalized Chua's circuit exhibiting n-scroll attractors has been accomplished. The dual-input describing functions of the piecewise-linear characteristics of Chua's diode have been obtained and based on the harmonic balance principle, the existence and the locations of the n-scrolls have been verified.

Hidden Attractor in Chua’s Circuits

“…It is also can be noted that to obtain existence of hidden attractor in Chua's circuit one can artificially stabilized (Suykens et al, 1997;Savaci & Gunel, 2006;Leonov et. al., 2010a) zero stationary point by inserting small stable zone around zero stationary point into nonlinearity (Chua diode characteristics).…”

Describing function based methods for predicting chaos in a class of fractional order differential equations

“…In fact, chaos is interpreted as a "noisy limit cycle" in the Genesio-Tesi conjecture. Now, more clarifications on this conjecture, which has been successfully applied to predict chaotic dynamics in nonlinear integer order systems [40][41][42][43][44], are given. Based on the GenesioTesi conjecture, four conditions should be fulfilled [40,41].…”

The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation

“…This approach for analysis of nonlinear systems is easily found in several classic books [Ogata, 1970;Slotine & Li, 1991;Khalil, 1996;Glad & Ljung, 2000], consisting of an extension of linear techniques based on the concepts of the frequency response in order to verify effects of certain nonlinearities on a feedback dynamic system. The analysis by describing functions allows to predict stability and the possible existence of limit cycles [Ogata, 1970;Oliveira et al, 2012] and chaotic behavior, which can be interpreted as an interaction between limit cycles and equilibrium points [Genesio & Tesi, 1991;Neymeyr & Seelig, 1991;Genesio & Tesi, 1992;Savacı & Günel, 2006]. The transfer function of the linear part of Chua's circuit between the output x and the input u (see Fig.…”