Memristor-Based N-Scroll Chaotic Systems And Circuit Simulations

With the rapid development of modern society, a lot of information has been emerging. It will be an important trend to strengthen the confidentiality of information transmission, to increase the intelligence of information processing and to reduce the volume and power consumption of the system in the future. Memristor, as a new circuit component, could promote to solve the problem. Memristors have many advantages such as nanoscale size, automatic memory and nonlinear characteristics. It is much better to introduce memristors to nonlinear circuits to construct a chaotic circuit system, which could be used in secret communication, weather forecast, image encryption and other fields. Because of memristors’advantages of automatic memory, nano size and facilitative integration, memristive neural networks can significantly reduce the size of the neural network and promote the ability of intelligent information processing.In this paper, the nonlinearity and memory of memristor are deeply investigated. The mathematics models and circuit models are studied, and their typical features are analyzed. Then, chaotic systems and circuits are constructed by combining memristors with nonlinear chaotic system. Finally, memristors are applied to neural network to implement its associative learning via memristive circuits. The main content of this paper includes the following five parts:(1) One of mathematical models of memristors is discussed. According to the mathematical models of HP memristors, a flux-controlled memristor is achieved. The SPICE model and circuit model of flux-controlled memristor are established and their simulations are given.(2) The characteristics of chaos are introduced, and the chaotic system of the flux-control memristor is studied, which chaotic attractors are observed. According to the mathematical model of chaotic system based on flux-control memristors, large numbers of experiments for these circuits are performed and some simulations are gotten, which show that expected chaotic attractors are found.(3) A new scroll chaotic system is designed by combining the HP memristor model with triangular wave series. Its chaotic attractors are gotten by the circuit simulation. The numerical analysis and the Lyapunov exponent of the system are studied, and the dynamic behaviors of the system is demonstrated by circuit simulation and computer simulations.(4) A time-delay chaotic system based on memristors is addressed under different conditions. A new chaotic random sequence generator is constructed, which can generate pseudo random sequences. An NIST test method is used to illustrate the pseudo randomness.(5) The artificial neural network based on a charge-controlled memristor is studied. A new learning algorithm named as the average input feedback method (AIF) is proposed. The associative memory is more clearly explained by improved Pavlovian experiment. A SPICE simulation model of the charge-controlled memristor is established to implement the circuitry of the memristor-based associative memory neural network.Finally, all the work of this paper is summarized, and the work is prospected.