الفهرس 
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Abstract
In this thesis we study chaos and synchronization in some nonlinear electronic circuits. Chaos appears in some nonlinear dynamical systems and is distinguished by sensitive dependence on initial conditions. Nonlinear electronic circuits play an important role in studying nonlinear phenomena such as chaotic dynamics and synchronization which have effective applications in secure communications and industry applications. We proposed a modified chaotic system that describes the dynamics of the modified Autonomous Duffing VanDer Pol (ADVP) circuit, by adding an Ohm?s resistor in parallel with the inductor of the original circuit. The modified circuit is said to be MADVP circuit and its system gives wider area of studying chaos. We give mathematical and numerical analysis of the dynamics for MADVP system by studying: the equilibrium points and their local stability using RouthHurwitz criterion; periodic solutions (the existence of Hopf bifurcation), and the stability of the periodic solutions (using the theorem given by Hs(Rh(Bu and Kazarinoff); determining the regions of chaotic motion; calculating Lyapunov exponents and fractal dimension. Finally, we applied different techniques of chaos synchronization on two identical MADVP systems such as Pecora and Carroll method, one way coupling, active control, adaptive active control and simple global synchronization. In addition to that we apply adaptive synchronization to two other chaotic circuits; the original Chua?s circuit and the modified Chua?s circuit with x|x| when the parameters are fully unknown or uncertain. Numerical simulations results are given to show the validity of the proposed synchronization schemes. The new results in this work are: (1) Modifying the ADVP circuit and having a generalized system called the MADVP system. (2) Studying the qualitative behavior of the solutions of the MADVP system. (3) Chaos synchronization of two identical MADVP systems using different methods. (4) Adaptive synchronization of Chua?s circuits with fully unknown parameters.