Research On Locally-active Memristors And Applications

Chua proposed the concept of memristors in 1970 s,but it was difficult to prove the existence of memristors due to the lack of experiments.Until HP Labs announced that the Ti O2 memristor had been fabricated in 2008,memristors attracted researchers’ attention worldwide.Memristor is a nonlinear resistor with memory,which has significant potential in applications such as non-volatile memories,chaotic oscillators,artificial neural networks,and digital logic circuits.Based on the theory of the memristors,Chua proposed the locally-active memristors,expounded that locally-active devices are essential components for amplifying infinitesimal fluctuation signals and maintaining oscillating,and concluded that local activity is the origin of complexity.In addition,the locally-active memristor can be used to simulate the behaviors of biological nerves,and the neural network working on the edge of chaos can optimize neural calculations and simulate accurately the actual characteristics of biological neural networks.Moreover,the non-volatile locally-active memristor can realize the computing in memory of neural network and break Von Neumann calculation system.Therefore,the locally-active memristor will be the key circuit element to realize a new generation integration of chaos-storage-computing in the future.At present,the research about chaotic neural network of computing in memory has just begun,and many basic theoretical issues need to be further studied,such as the modeling and analysis of locally-active memristors,the edge of chaos mechanism and the design of chaotic oscillating modules.In this thesis,a novel locally-active memristor model is proposed.Based on the locally-active memristor model,a periodic oscillator is designed,and a chaotic oscillating circuit is designed on the basis of the periodic oscillator.Finally,it is used in digital watermarking technology.The main works of this thesis are as follows:(1)Based on the locally-active theorem and Chua’s unfolding principle,a non-volatile locally-active memristor model is proposed.Using the power-off plot(POP)and DC V-I plot,it is found that it has two asymptotically stable equilibrium points(i.e.,two non-volatile memristance),with globally-passive but locally-active characteristics.(2)At the locally-active operating point of the memristor,a small signal equivalent circuit showing its the characteristics near the operaing point is derived.By using the small signal equivalent circuit,we show that the memristor is located in edge of chaos over a certain voltage range.According to the small-signal equivalent circuit and Hopf bifurcation theory,it is theoretically analyzed that when the memristor is connected with an inductor in series,the circuit will undergo Hopf bifurcation and the memristor will oscillate near the locally-active operating point in the edge of chaos region.The oscillating frequency and the external inductance in series can be calculated based on the small-signal equivalent circuit admittance Y(iω)and its frequency characteristics.(3)Considering the parasitic capacitance of the memristor in the periodic oscillating circuit,a third-order chaotic oscillating circuit is constructed.Therefore,a chaotic oscillating circuit is designed on the basis of the periodic oscillating circuit.We analyzed the complex dynamics of the chaotic system using the methods of Lyapunov exponent spectum,bifurcation diagram and basin of attraction.(4)Based on chaotic sequence of the locally-active memristor,an image watermarking technique based on chaotic encryption and discrete wavelet transform is proposed to embed and extract digital watermarks of color images.