Memristor simulator and applications

The memristor is a two-terminal element that provides the functional relationship between charge and flux. It was first described by Chua in 1971 as a basic non-linear circuit element. After announcing that Stanley Williams and his group of HP Labs realized a nano-scale TiO2 passive memristor element with the characteristics described by the memristor theory, studies on potential applications of memristor such as sensors, memory devices, cellular neural networks, analog circuits and chaotic circuits has increased among scientists around the world. However, the TiO2 memristor is not currently available as a commercial product due to the financial and technical difficulties encountered in the production of nanoscale devices. Many theoretical models for describing and implementing memristive behavior in circuit applications have been included in the literature. Mathematical models and SPICE models covering most of them can not be used in physical applications. For this reason, active memristor emulator circuits, which mimic the dynamic behavior of the TiO2 memristor, have begun to take place in the literature. In this study, two memristance simulator circuits are proposed, which provides a non-linear relationship between flux and charge, as proposed by Chua. The memristive characteristics of designed circuits have been verified by SPICE simulations and experimental studies. One of the designed circuits is CCII+ based and floating. The other is based on DO-OTA, floating and electronically controllable. They are both xvi simple and convenient to implement with off-the-shelf integrated circuits. Operating frequency ranges are broader than most similar studies in the literature. In order to verify the operability of the designed structures, the implementation and analysis of the chaotic circuits which their non-linear term is provided by the memristance value have been studied. Chaotic circuits are especially a key component for safe communication systems and modeling of complex events. The double scroll Chua chaotic attractor which is widely studied in the literature and Rössler chaotic attractor are implemented with the designed CCII+ based memristance simulator circuit. Mathematical analysis such as bifurcation diagrams, equilibrium points and Lyapunov exponents were performed in MATLAB environment and on-board experiment are performed with again commercially available components. It has been proven that mathematical analysis and experimental results are verified each other. The adapability of the proposed memristance simulator circuits is also shown by these studies. Finally, random number generator design, which is one of the useage areas in the fields of chaos circuits, has been studied. The realization of a low-precision, high-performance, true random number generator is achieved by sampling the designed double-scroll chaotic signal with ADCs on the market. The resulting bit sequence was successfully passed the NIST-800-22 statistical test package and the random structure was verified.