Design of memristor based chaotic systems and application to chaotic communication systems

Memristor, which was presented as the fourth basic circuit element after resistor, inductor and capasitor to the literature by Leon O. Chua, takes its name from the combination of the words MEMory and ResISTOR. This element, which basically links a relationship between flux and charge, has a dynamic, and, generally a nonlinear relationship between the current and voltage of it. The memristor is a volatile/non-volatile, nanoscale and programmable component, whose resistance changes as a function of its inherent dynamic variable, voltage across and/or the current through it. Since this element is not yet fully manufactured as a commercial product, emulator circuits that exhibit a memristor feature are introduced to the literature and further investigations are conducted with the help of these circuits. In this study, a smooth, continuous and nonlinear flux-controlled memristor emulator is used and utilized in five different memristor based chaotic and hyperchaotic circuits selected from the literature. State equations, phase portraits, Lyapunov exponents and bifurcation diagrams of the modified circuits employing the proposed memristor emulator have been examined in detail. The electronic circuit models and design of the modified chaotic circuits obtained are implemented in PSpice, Multisim and LTspice programs, and have been also obtained in real time in a laboratory environment. The proposed chaotic and hyperchaotic systems have been designed on the FPGA (Field Programmable Gate Array) platform and implemented as hardware. Theoretical, simulation, and real-time analyses clearly show that the chaotic and hyperchaotic circuits presented are capable of demonstrating rich chaotic dynamic properties. Chaotic signals are widely used in communication systems, especially for masking information-carrying waveforms, because they have a wide band frequency spectrum, a non-periodic time series characteristics, and therefore similar to noise in terms of unpredictability. Within the scope of the thesis, various applications of designed memristor based chaotic and hyperchaotic systems have been implemented in both analog and digital communication systems. In order to realize chaotic synchronization in an analog communication application, a proportional-integral-derivative (PID) controller design has been carried out using different optimization algorithms such as Firefly (FA) and Genetic Algorithm (GA). The analog communication application has been performed by using the signals obtained via analog modulation. In the digital communication application, various implementations have been realized based on differential chaos shift keying (DCSK) and FPGA based chaotic on-off keying (COOK) modulation. After designing AM-DCSK and FM-DCSK simulators in MATLAB, application of memristor based chaotic and hyperchaotic systems has been realized employing these simulators. The noise performance analysis of these simulators is obtained and presented under the AWGN channel.