Electrical - Electronic Engineering / Elektrik - Elektronik Mühendisliği
Permanent URI for this collectionhttps://hdl.handle.net/11147/11
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Article Citation - WoS: 12Citation - Scopus: 15Harmonic Balance Analysis of the Generalized Chua's Circuit(World Scientific Publishing Co. Pte Ltd, 2006) Savacı, Ferit Acar; Günel, SerkanIn 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.Article Citation - WoS: 2Citation - Scopus: 2Determination of the Stationary State Densities of the Stochastic Nonlinear Dynamical Systems(Elsevier Ltd., 2006) Günel, Serkan; Savacı, Ferit AcarThe stationary state probability densities appear not only in the study of dynamical systems with random vector fields, but also in the deterministic dynamical systems exhibiting chaotic behavior when the uncertainties in the initial conditions are represented with the probability densities. But since it is very hard problem to determine these densities, in this paper the new efficient method to obtain an approximate solution of Fokker-Planck-Kolmogorov equation which arises in the determination of the stationary state probability densities has been given by representing the densities with compactly supported functions. With specific choice of the compactly supported functions as piecewise multivariable polynomials which are supported on the ellipsoidal regions, the parameters to be calculated for determining the densities can be considerably decreased compared to Multi-Gaussian Closure scheme, in which the stationary densities are assumed to be the weighted average of the Gaussian densities. The main motivation to choose the compactly supported functions is that, in the chaotic dynamics the states are trapped in a specific compact subspace of the state space. The stationary state densities of two basic examples commonly considered in the literature have been estimated using the Parzen's estimator, and the densities obtained using the newly proposed method have been compared with these estimated densities and the densities obtained with the Multi-Gaussian Closure scheme. The results indicate that the presented compactly supported piecewise polynomial scheme can be successful compared to Multi-Gaussian scheme, when the system is highly nonlinear.Conference Object Citation - WoS: 3Citation - Scopus: 6Approximate Stationary Density of the Nonlinear Dynamical Systems Excited With White Noise(Institute of Electrical and Electronics Engineers Inc., 2005) Günel, Serkan; Savacı, Ferit AcarIn this paper, obtaining approximate solution of Fokker-Planck-Kolmogorov (FPK) Equation using compactly supported functions has been discussed. With specific choice of such functions as piecewise multivariable polynomials which are supported on ellipsoidal regions, the parameters to be determined can be considerably decreased compared to Multi- Gaussian Closure scheme [1]. An example commonly considered in the literature has been analyzed and the proposed method has been compared with the Multi-Gaussian Closure scheme. The simulation results indicate that the new scheme is quite successful even if the driving noise is not white Gaussian, but has an exponential correlation function with small correlation time.