Simulation and realization of the multi-mode chaotic behaviors

ABSTRACT PhD Thesis SIMULATION AND REALIZATIN OF THE MULTI-MODE CHAOTIC BEHAVIORS Mustafa TURK Fırat University Graduate School of Natural and Applied Science Department of Electrical and Electronics Engineering 2004, Pages: 88 Chua's circuit takes important place in the nonlinear system theory because of one of the first systems developed to examine chaotic behaviors. Examining the dynamics of the Chua's circuit, it is observed that dynamics are restricted with equilibrium points that related to the nonlinear element in the system. To increase the variety of the circuit behaviors, characteristic of the nonlinear element in the circuit have to been changed. The most important factor determining the equilibrium points in the circuit is the numbers of the breaking points of the nonlinear element. In this thesis, third order generalized Chua's circuit equation is used. Nonlinear element in the system is selected as Piece-wise linear element that breaking points can be change. Two identical multi-breaking point and piece-wise linear elements controlled with jc- and y- state- space variables are added to the system. Under effect of the addition breaking points, new equilibrium points are originated. These equilibrium points are graphically drawn and mathematically calculated. New equilibrium points are originated on the both x- and y-axes, chaotic attractors originated around these equilibrium points are called as n+n scroll chaotic attractors. Removing from the system the multi-breaking point and piece-wise linear element controlled with jc- state-space variable, chaotic attractors are observed only on the y=-x line. Chaotic scrolls originated around the equilibrium points are called as two dimensional n- scroll chaotic attractors. XIIThese behaviors are theoretically examined at first. Also, developed behaviors are experimentally obtained in order to use real applications. Current feedback operational amplifiers are preferred in the experimental circuits, because of obtaining wide bandwidth. However, obtained experimental results are verified by Pspice program results. Furthermore, synchronization of these chaotic attractors is achieved using Pecora and Carroll synchronization method Key Words: Chaos, Chua's circuit, chaos synchronization, n+n scroll chaotic attractors, n- scroll chaotic attractors, multi-mode chaotic systems, nonlinear systems, piecewise linear systems. XIII