الفهرس | Only 14 pages are availabe for public view |
Abstract In recent decades, the move towards the utilization of chaotic systems has flourished in various engineering applications. Hence, there is an increasing demand on generalized, modified and novel chaotic systems. Moreover, the development of non-integer or fractional-order calculus and chaos theory, the fractional order chaotic systems have become a useful way to evaluate characteristics of dynamical systems and forecast the trend of complex systems. In this direction, this thesis is primarily concerned with the study of the effects of different parameters on the type of the response of each chaotic systems are investigated through numerical simulations of time series, phase portraits, bifurcations, and Maximum Lyapunov Exponent (MLE) values against all system parameters. In addition, the integerorder chaotic systems and fractional-order chaotic systems can be implemented using circuit realization with Pspice software, Field Programmable Analog Gate (FPGA), and Field Programmable Analog Array (FPAA). The obtained results show that the fractional order chaotic attractors from MATLAB, Pspice software, FPGA, and FPAA are the same. By utilizing the fractional calculus theory and computer simulations, it is found that chaos exists in the fractional order threedimensional system with order less than three. It is worth mentioning that the results are validated by the existence of one positive Lyapunov exponent, phase diagrams. In order to verify the effectiveness of the proposed system, an electronic circuit is designed with the purpose of synthesizing the fractional-order chaotic system. The fractional order integral is realized with an electronic circuit based on the synthesis of a fractance circuit. The realization has been done via synthesis as passive RC circuits connected to an operational amplifier. The continuous fractional expansion has been utilized on a fractional integration transfer function, which has been approximated to an integer order rational transfer function considering the charef approximation, and Matsuda approximation. The analogue electronic circuits have been simulated using PSpice. In addition, we use the FPGA and FPAA to produce the fractional order chaotic system attractors. The FPGA of the proposed system is realized based on Verilog HDL, Xilinx ISE 14.7 and Xilinx FPGA Artix-7 XC7A100T. In addition, the FPAA of the proposed system can be implemented using the Anadigm AN231E04 FPAA with Anadigm Designer 2 (EDA) software. Cancellable face recognition based on proposed fractional-order chaotic system has been implemented on FERET, LFW, and ORL datasets, and the results are compared with those of other schemes. |