Emulating Electrical Characteristics Of Memristor And Its Applications In Chaotic System

The memristor, next to the rest of the more familiar circuit elements such as theresistor, the capacitor, and the inductor, is considered as the fourth circuit element. Itis a two terminal element to set up a mathematical relationship between the magneticflux φ and the electric charge q. The memory behavior of the memristor can beinterpreted by the fact that its resistance depends on the history of the current havingpassed through it. Since a solid state memristor was fabricated in Hewlett-Packard(HP) laboratory, immense research interests have been inspired due to its potentialapplications in various fields such as nonvolatile RAM, computers, artifical neuralnetwork, and electronics.Since commercially available memristors are not expected to appear in the nearfuture owing to the cost and technical difficulties in fabricating nano-scale devices, itis useful to have a memristor emulator, which behaves like a real memristor, to buildreal-world application circuits which explore and exploit memristor’s potentials.Furthermore, the memristor is a nonlinear element in itself, so it can be employed torealize high frequency chaotic oscillators. In this dissertation, we focus mainly onemulating electrical characteristics of the memristor and studying its applications inchaotic systems. The main study and contributions are given as follows:(1) Based on the physical model of HP memristor, an analogue model of charge-controlled memristors is proposed in this paper. The Pspice simulation results showthe electrical characteristics of the proposed emulator are well consistent with those ofthe HP memristor. The proposed emulator built with off-the-shelf components is verysuitable for experimentally analysing and researching real-word application circuitswith memristors. Because memory effects are ubiquitous in nano-devices, thecapacitor and the inductor with nano-scale have similar characteristics to memristors,and their internal states also display obvious memory effects. In order to simulatefeatures of all the mem-elements, a universal emulator is implemented withoff-the-shelf components. It can transform the grounded memristor into a floatingmemristor, or a floating meminductor, or a floating memcapacitor by connectingdifferent components to it. Because the universal emulator is floating, it is notrestricted to be grounded and can be connected between any two voltages.(2) A systematic design approach for memristor-based chaotic circuits is introducedin this paper. We think a memristive chaotic circuit can be implemented with three functional blocks, namely, a sinusoidal oscillator, an RC phase-shift network, and anonlinear network (implemented with memristor). Many novel memristive chaoticcircuits can be obtained by using different sinusoidal oscillators. The second-orderWien-bridge oscillator and the third-order Twin-T oscillator acted as design examplesare provided to verify our scheme.(3) Due to having only a positive Lyapunov exponent, all of the existingmemristor-based chaotic circuits cannot generate hyperchaotic behaviors. Amemristor-based hyperchaotic circuit, by replacing the nonlinear resistor in MCKcircuit with a flux-controlled memristor, is also presented. The dynamical behaviorsare numerically verified through investigating phase portraits, Poincare maps,Lyapunov exponents, and bifurcation diagram. In order to confirm the occurrence ofhyperchaotic behaviours in this circuit, an analog realization of the piecewise-linearflux-controlled memristor is proposed and Pspice simulations are conducted on theresulting circuit.(4) A modified state-controlled cellular nonlinear network (SC-CNN) cell, whoseoutput nonlinear function is implemented with the intrinsic nonlinearity of memristor,is introduced in this paper. By using the appropriate connection of three modifiedSC-CNN cells, a SC-CNNs-based memristive chaotic circuit is developed. Inparticular, an imitative memristive circuit is introduced to experimentally investigatethe dynamical behaviors. The resemblance of experimental results with those ofnumerical simulations shows that the memristive chaotic circuit can be efficientlyimplemented in terms of SC-CNN scheme.(5) In order to deal with the problem of synchronization of the memristor-basedchaotic system, we present an adaptive control scheme for the synchronization ofidentical chaotic systems with uncertain system parameters. Adopting the systemparameter modulation technology, a new secure communication system based onadaptive synchronization is illustrated. The feasibility of this secure communicationsystem is verified by numerical simulations.