Implementation of fractional order chaotic system with active circuit elements

In this master's thesis, a MATLAB/M-file was developed for fractional chaotic systems using the Grünwald-Letnikov definition, and simulations of fractional chaotic systems, which have been extensively studied in the literature, were carried out in the form of state space diagrams and time responses of state variables. In addition, bifurcation and bifurcation points in these systems are theoretically obtained according to the fractional order q system order, and thus, the system degrees where chaotic behavior is expected and chaotic behavior will not be observed are tested with simulations. In addition to these, chain fractance structure used for analog circuit designs of fractional order chaotic systems is mentioned and chain fractance designs are obtained with converged integer order transfer functions of fractional integral operator. Analogue circuit designs of two different fractional chaotic systems, namely the fractional order Lorenz and Chen systems, were carried out using the obtained chain fractance. Simulations of the designed analog circuits were carried out from the ORCHAD/Pspice environment. It has been shown that the simulation results obtained by developing the MATLAB/M-file are confirmed by the results of the ORCHAD/Pspice analog circuit application.