الفهرس 
Chapter 1:IntroductionOnly 14 pages are availabe for public view
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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.