الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Many circuit applications utilize nonlinear circuit elements such as nonlinear resistors, nonlinear capacitors, and nonlinear inductors of voltage or current controlled types. Such non-linearities made these circuits prone to chaotic behavior. Chaos is a type of behavior that is not periodic, quasi-periodic nor random with the property of sensitive dependence on initial condition and it needs a special type of treatment far from error accumulation, false convergence, etc. This thesis presents an algorithm for analyzing electrical, electronic and microwave circuits containing linear and nonlinear elements. The analysis procedure makes use of the normal form methods applied to the analyzed circuit or network. The simplicity of the normal form equations describing the network makes one able to get rid of the problems associated with long transient, stiff system of differential equations (dispersion of eigenvalues), numerical instabilities, and lack of convergence. Different types of normal forms are introduced, namely, Jordan, rational, Poincare’, Ushiki, Chua, and Takens normal forms Rules for using each are classified. Algorithms are mechanized using Maple package. Several examples (each represents a class) were solved, compared with classical algorithms, and showed an excellence over the emaing algorithms. The proposed algorithm also offers closed form solutions for a class of linear and nonlinear circuits. The applicability of the algorithm is not only including circuits network 1t it also can be used without major modifications to any dynamical system by its state equations. One more advantage of this work is that it overcome drawbacks associated with the determination of eigenvalues Finally method offers simplicity, accuracy and easy implementations The method of normal forms classifies the vector field near the singular point, and the normal form consists of the resonant vectors. Characterized by the linear part of the system, it is also consists of non-resonant vector field that can not be studied using classical linearization methods.